Compute the value of each of the following. a. F 15 b. F 15 − 2 c. F 15 − 2 d. F 1515 e. F 15 / 5

Question

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Answer 1

Textbook Question

Chapter 13, Problem 1E

Compute the value of each of the following.

a. $F 15$

b. $F 15 − 2$

c. $F 15 − 2$

d. $F 1515$

e. $F 15 / 5$

Expert Solution

To determine

(a)

To calculate:

The value of $F15$ .

Answer to Problem 1E

Solution:

The value of $F15$ is 610.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Calculation:

The $15th$ term in the sequence is the sum of $13th$ and $14th$ term. By using recursive formula,

$FN=FN−1+FN−2$

Substitute 1 for $F1$ and $F2$ in the above recursive formula to calculate $F3$ ,

$F3=1+1=2$

Substitute 1 for $F2$ and 2 for $F3$ to calculate $F4$ ,

$F4=1+2=3$

Substitute 2 for $F3$ and 3 for $F4$ to calculate $F5$ ,

$F5=2+3=5$

Similarly, $F6=8$ , $F7=13$ , $F8=21$ , $F9=34$ , $F10=55$ , $F11=89$ , $F12=144$ , $F13=233$ , and $F14=377$ are obtained.

Substitute $F13$ and $F14$ in the above recursive formula to calculate $F15$ .

$F15=233+377=610$

Conclusion:

Thus, the $15th$ term in the sequence is 610.

Expert Solution

To determine

(b)

To calculate:

The value of $F15−2$ .

Answer to Problem 1E

Solution:

The value of $F15−2$ is 608.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15−2$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Substitute 610 for $F15$ from part (a) to calculate $F15−2$ ,

$F15−2=610−2=608$

Conclusion:

Thus, the value of $F15−2$ is 608.

Expert Solution

To determine

(c)

To calculate:

The value of $F15−2$ .

Answer to Problem 1E

Solution:

The value of $F15−2$ is 233.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15−2$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

In the Fibonacci sequence $F15−2$ is the $13th$ term of the sequence.

Substitute 89 for $F11$ and 144 for $F12$ from part (a) to calculate $F13$ ,

$F13=89+144=233.$

Conclusion:

Thus, the value of $F15−2$ is 233.

Expert Solution

To determine

(d)

To calculate:

The value of $F1515$ .

Answer to Problem 1E

Solution:

The value of $F1515$ is 122.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F1515$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Substitute 610 for $F15$ from part (a) to get $F1515$ ,

$F1515=61015=40.67$

Conclusion:

Thus, the value of $F1515$ is $40.67$ .

Expert Solution

To determine

(e)

To calculate:

The value of $F15/5$ .

Answer to Problem 1E

Solution:

The value of $F15/5$ is 2.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15/5$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

The number $F15/5$ is the third term of the sequence given by,

$F15/5=F3=F2+F1=1+1=2$

Conclusion:

Thus, the value of $F15/5$ is 2.

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Answer 2

Textbook Question

Chapter 13, Problem 1E

Compute the value of each of the following.

a. $F 15$

b. $F 15 − 2$

c. $F 15 − 2$

d. $F 1515$

e. $F 15 / 5$

Expert Solution

To determine

(a)

To calculate:

The value of $F15$ .

Answer to Problem 1E

Solution:

The value of $F15$ is 610.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Calculation:

The $15th$ term in the sequence is the sum of $13th$ and $14th$ term. By using recursive formula,

$FN=FN−1+FN−2$

Substitute 1 for $F1$ and $F2$ in the above recursive formula to calculate $F3$ ,

$F3=1+1=2$

Substitute 1 for $F2$ and 2 for $F3$ to calculate $F4$ ,

$F4=1+2=3$

Substitute 2 for $F3$ and 3 for $F4$ to calculate $F5$ ,

$F5=2+3=5$

Similarly, $F6=8$ , $F7=13$ , $F8=21$ , $F9=34$ , $F10=55$ , $F11=89$ , $F12=144$ , $F13=233$ , and $F14=377$ are obtained.

Substitute $F13$ and $F14$ in the above recursive formula to calculate $F15$ .

$F15=233+377=610$

Conclusion:

Thus, the $15th$ term in the sequence is 610.

Expert Solution

To determine

(b)

To calculate:

The value of $F15−2$ .

Answer to Problem 1E

Solution:

The value of $F15−2$ is 608.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15−2$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Substitute 610 for $F15$ from part (a) to calculate $F15−2$ ,

$F15−2=610−2=608$

Conclusion:

Thus, the value of $F15−2$ is 608.

Expert Solution

To determine

(c)

To calculate:

The value of $F15−2$ .

Answer to Problem 1E

Solution:

The value of $F15−2$ is 233.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15−2$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

In the Fibonacci sequence $F15−2$ is the $13th$ term of the sequence.

Substitute 89 for $F11$ and 144 for $F12$ from part (a) to calculate $F13$ ,

$F13=89+144=233.$

Conclusion:

Thus, the value of $F15−2$ is 233.

Expert Solution

To determine

(d)

To calculate:

The value of $F1515$ .

Answer to Problem 1E

Solution:

The value of $F1515$ is 122.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F1515$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Substitute 610 for $F15$ from part (a) to get $F1515$ ,

$F1515=61015=40.67$

Conclusion:

Thus, the value of $F1515$ is $40.67$ .

Expert Solution

To determine

(e)

To calculate:

The value of $F15/5$ .

Answer to Problem 1E

Solution:

The value of $F15/5$ is 2.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15/5$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

The number $F15/5$ is the third term of the sequence given by,

$F15/5=F3=F2+F1=1+1=2$

Conclusion:

Thus, the value of $F15/5$ is 2.

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Answer 3

Textbook Question

Chapter 13, Problem 1E

Compute the value of each of the following.

a. $F 15$

b. $F 15 − 2$

c. $F 15 − 2$

d. $F 1515$

e. $F 15 / 5$

Expert Solution

To determine

(a)

To calculate:

The value of $F15$ .

Answer to Problem 1E

Solution:

The value of $F15$ is 610.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Calculation:

The $15th$ term in the sequence is the sum of $13th$ and $14th$ term. By using recursive formula,

$FN=FN−1+FN−2$

Substitute 1 for $F1$ and $F2$ in the above recursive formula to calculate $F3$ ,

$F3=1+1=2$

Substitute 1 for $F2$ and 2 for $F3$ to calculate $F4$ ,

$F4=1+2=3$

Substitute 2 for $F3$ and 3 for $F4$ to calculate $F5$ ,

$F5=2+3=5$

Similarly, $F6=8$ , $F7=13$ , $F8=21$ , $F9=34$ , $F10=55$ , $F11=89$ , $F12=144$ , $F13=233$ , and $F14=377$ are obtained.

Substitute $F13$ and $F14$ in the above recursive formula to calculate $F15$ .

$F15=233+377=610$

Conclusion:

Thus, the $15th$ term in the sequence is 610.

Expert Solution

To determine

(b)

To calculate:

The value of $F15−2$ .

Answer to Problem 1E

Solution:

The value of $F15−2$ is 608.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15−2$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Substitute 610 for $F15$ from part (a) to calculate $F15−2$ ,

$F15−2=610−2=608$

Conclusion:

Thus, the value of $F15−2$ is 608.

Expert Solution

To determine

(c)

To calculate:

The value of $F15−2$ .

Answer to Problem 1E

Solution:

The value of $F15−2$ is 233.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15−2$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

In the Fibonacci sequence $F15−2$ is the $13th$ term of the sequence.

Substitute 89 for $F11$ and 144 for $F12$ from part (a) to calculate $F13$ ,

$F13=89+144=233.$

Conclusion:

Thus, the value of $F15−2$ is 233.

Expert Solution

To determine

(d)

To calculate:

The value of $F1515$ .

Answer to Problem 1E

Solution:

The value of $F1515$ is 122.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F1515$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Substitute 610 for $F15$ from part (a) to get $F1515$ ,

$F1515=61015=40.67$

Conclusion:

Thus, the value of $F1515$ is $40.67$ .

Expert Solution

To determine

(e)

To calculate:

The value of $F15/5$ .

Answer to Problem 1E

Solution:

The value of $F15/5$ is 2.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15/5$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

The number $F15/5$ is the third term of the sequence given by,

$F15/5=F3=F2+F1=1+1=2$

Conclusion:

Thus, the value of $F15/5$ is 2.

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Answer 4

Textbook Question

Chapter 13, Problem 1E

Compute the value of each of the following.

a. $F 15$

b. $F 15 − 2$

c. $F 15 − 2$

d. $F 1515$

e. $F 15 / 5$

Expert Solution

To determine

(a)

To calculate:

The value of $F15$ .

Answer to Problem 1E

Solution:

The value of $F15$ is 610.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Calculation:

The $15th$ term in the sequence is the sum of $13th$ and $14th$ term. By using recursive formula,

$FN=FN−1+FN−2$

Substitute 1 for $F1$ and $F2$ in the above recursive formula to calculate $F3$ ,

$F3=1+1=2$

Substitute 1 for $F2$ and 2 for $F3$ to calculate $F4$ ,

$F4=1+2=3$

Substitute 2 for $F3$ and 3 for $F4$ to calculate $F5$ ,

$F5=2+3=5$

Similarly, $F6=8$ , $F7=13$ , $F8=21$ , $F9=34$ , $F10=55$ , $F11=89$ , $F12=144$ , $F13=233$ , and $F14=377$ are obtained.

Substitute $F13$ and $F14$ in the above recursive formula to calculate $F15$ .

$F15=233+377=610$

Conclusion:

Thus, the $15th$ term in the sequence is 610.

Expert Solution

To determine

(b)

To calculate:

The value of $F15−2$ .

Answer to Problem 1E

Solution:

The value of $F15−2$ is 608.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15−2$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Substitute 610 for $F15$ from part (a) to calculate $F15−2$ ,

$F15−2=610−2=608$

Conclusion:

Thus, the value of $F15−2$ is 608.

Expert Solution

To determine

(c)

To calculate:

The value of $F15−2$ .

Answer to Problem 1E

Solution:

The value of $F15−2$ is 233.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15−2$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

In the Fibonacci sequence $F15−2$ is the $13th$ term of the sequence.

Substitute 89 for $F11$ and 144 for $F12$ from part (a) to calculate $F13$ ,

$F13=89+144=233.$

Conclusion:

Thus, the value of $F15−2$ is 233.

Expert Solution

To determine

(d)

To calculate:

The value of $F1515$ .

Answer to Problem 1E

Solution:

The value of $F1515$ is 122.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F1515$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Substitute 610 for $F15$ from part (a) to get $F1515$ ,

$F1515=61015=40.67$

Conclusion:

Thus, the value of $F1515$ is $40.67$ .

Expert Solution

To determine

(e)

To calculate:

The value of $F15/5$ .

Answer to Problem 1E

Solution:

The value of $F15/5$ is 2.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15/5$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

The number $F15/5$ is the third term of the sequence given by,

$F15/5=F3=F2+F1=1+1=2$

Conclusion:

Thus, the value of $F15/5$ is 2.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution

To determine

(a)

To calculate:

The value of $F15$ .

Answer to Problem 1E

Solution:

The value of $F15$ is 610.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Calculation:

The $15th$ term in the sequence is the sum of $13th$ and $14th$ term. By using recursive formula,

$FN=FN−1+FN−2$

Substitute 1 for $F1$ and $F2$ in the above recursive formula to calculate $F3$ ,

$F3=1+1=2$

Substitute 1 for $F2$ and 2 for $F3$ to calculate $F4$ ,

$F4=1+2=3$

Substitute 2 for $F3$ and 3 for $F4$ to calculate $F5$ ,

$F5=2+3=5$

Similarly, $F6=8$ , $F7=13$ , $F8=21$ , $F9=34$ , $F10=55$ , $F11=89$ , $F12=144$ , $F13=233$ , and $F14=377$ are obtained.

Substitute $F13$ and $F14$ in the above recursive formula to calculate $F15$ .

$F15=233+377=610$

Conclusion:

Thus, the $15th$ term in the sequence is 610.

Expert Solution

To determine

(b)

To calculate:

The value of $F15−2$ .

Answer to Problem 1E

Solution:

The value of $F15−2$ is 608.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15−2$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Substitute 610 for $F15$ from part (a) to calculate $F15−2$ ,

$F15−2=610−2=608$

Conclusion:

Thus, the value of $F15−2$ is 608.

Expert Solution

To determine

(c)

To calculate:

The value of $F15−2$ .

Answer to Problem 1E

Solution:

The value of $F15−2$ is 233.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15−2$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

In the Fibonacci sequence $F15−2$ is the $13th$ term of the sequence.

Substitute 89 for $F11$ and 144 for $F12$ from part (a) to calculate $F13$ ,

$F13=89+144=233.$

Conclusion:

Thus, the value of $F15−2$ is 233.

Expert Solution

To determine

(d)

To calculate:

The value of $F1515$ .

Answer to Problem 1E

Solution:

The value of $F1515$ is 122.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F1515$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Substitute 610 for $F15$ from part (a) to get $F1515$ ,

$F1515=61015=40.67$

Conclusion:

Thus, the value of $F1515$ is $40.67$ .

Expert Solution

To determine

(e)

To calculate:

The value of $F15/5$ .

Answer to Problem 1E

Solution:

The value of $F15/5$ is 2.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15/5$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

The number $F15/5$ is the third term of the sequence given by,

$F15/5=F3=F2+F1=1+1=2$

Conclusion:

Thus, the value of $F15/5$ is 2.

Answer 8

Expert Solution

To determine

(a)

To calculate:

The value of $F15$ .

Answer to Problem 1E

Solution:

The value of $F15$ is 610.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Calculation:

The $15th$ term in the sequence is the sum of $13th$ and $14th$ term. By using recursive formula,

$FN=FN−1+FN−2$

Substitute 1 for $F1$ and $F2$ in the above recursive formula to calculate $F3$ ,

$F3=1+1=2$

Substitute 1 for $F2$ and 2 for $F3$ to calculate $F4$ ,

$F4=1+2=3$

Substitute 2 for $F3$ and 3 for $F4$ to calculate $F5$ ,

$F5=2+3=5$

Similarly, $F6=8$ , $F7=13$ , $F8=21$ , $F9=34$ , $F10=55$ , $F11=89$ , $F12=144$ , $F13=233$ , and $F14=377$ are obtained.

Substitute $F13$ and $F14$ in the above recursive formula to calculate $F15$ .

$F15=233+377=610$

Conclusion:

Thus, the $15th$ term in the sequence is 610.

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

(a)

To calculate:

The value of $F15$ .

Answer 13

Answer to Problem 1E

Solution:

The value of $F15$ is 610.

Answer 14

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Calculation:

The $15th$ term in the sequence is the sum of $13th$ and $14th$ term. By using recursive formula,

$FN=FN−1+FN−2$

Substitute 1 for $F1$ and $F2$ in the above recursive formula to calculate $F3$ ,

$F3=1+1=2$

Substitute 1 for $F2$ and 2 for $F3$ to calculate $F4$ ,

$F4=1+2=3$

Substitute 2 for $F3$ and 3 for $F4$ to calculate $F5$ ,

$F5=2+3=5$

Similarly, $F6=8$ , $F7=13$ , $F8=21$ , $F9=34$ , $F10=55$ , $F11=89$ , $F12=144$ , $F13=233$ , and $F14=377$ are obtained.

Substitute $F13$ and $F14$ in the above recursive formula to calculate $F15$ .

$F15=233+377=610$

Conclusion:

Thus, the $15th$ term in the sequence is 610.

Answer 15

Expert Solution

To determine

(b)

To calculate:

The value of $F15−2$ .

Answer to Problem 1E

Solution:

The value of $F15−2$ is 608.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15−2$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Substitute 610 for $F15$ from part (a) to calculate $F15−2$ ,

$F15−2=610−2=608$

Conclusion:

Thus, the value of $F15−2$ is 608.

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

(b)

To calculate:

The value of $F15−2$ .

Answer 20

Answer to Problem 1E

Solution:

The value of $F15−2$ is 608.

Answer 21

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15−2$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Substitute 610 for $F15$ from part (a) to calculate $F15−2$ ,

$F15−2=610−2=608$

Conclusion:

Thus, the value of $F15−2$ is 608.

Answer 22

Expert Solution

To determine

(c)

To calculate:

The value of $F15−2$ .

Answer to Problem 1E

Solution:

The value of $F15−2$ is 233.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15−2$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

In the Fibonacci sequence $F15−2$ is the $13th$ term of the sequence.

Substitute 89 for $F11$ and 144 for $F12$ from part (a) to calculate $F13$ ,

$F13=89+144=233.$

Conclusion:

Thus, the value of $F15−2$ is 233.

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

(c)

To calculate:

The value of $F15−2$ .

Answer 27

Answer to Problem 1E

Solution:

The value of $F15−2$ is 233.

Answer 28

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15−2$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

In the Fibonacci sequence $F15−2$ is the $13th$ term of the sequence.

Substitute 89 for $F11$ and 144 for $F12$ from part (a) to calculate $F13$ ,

$F13=89+144=233.$

Conclusion:

Thus, the value of $F15−2$ is 233.

Answer 29

Expert Solution

To determine

(d)

To calculate:

The value of $F1515$ .

Answer to Problem 1E

Solution:

The value of $F1515$ is 122.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F1515$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Substitute 610 for $F15$ from part (a) to get $F1515$ ,

$F1515=61015=40.67$

Conclusion:

Thus, the value of $F1515$ is $40.67$ .

Answer 30

Expert Solution

Answer 31

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

(d)

To calculate:

The value of $F1515$ .

Answer 34

Answer to Problem 1E

Solution:

The value of $F1515$ is 122.

Answer 35

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F1515$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

Substitute 610 for $F15$ from part (a) to get $F1515$ ,

$F1515=61015=40.67$

Conclusion:

Thus, the value of $F1515$ is $40.67$ .

Answer 36

Expert Solution

To determine

(e)

To calculate:

The value of $F15/5$ .

Answer to Problem 1E

Solution:

The value of $F15/5$ is 2.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15/5$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

The number $F15/5$ is the third term of the sequence given by,

$F15/5=F3=F2+F1=1+1=2$

Conclusion:

Thus, the value of $F15/5$ is 2.

Answer 37

Expert Solution

Answer 38

Expert Solution

Answer 39

Expert Solution

Answer 40

To determine

(e)

To calculate:

The value of $F15/5$ .

Answer 41

Answer to Problem 1E

Solution:

The value of $F15/5$ is 2.

Answer 42

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The $Nth$ term of the Fibonacci sequence is denoted by $FN$ .

Given:

The given expression is $F15/5$ .

Formula used:

The recursive formula to calculate the $Nth$ Fibonacci number is given by,

$FN=FN−1+FN−2$

Here $FN−1$ and $FN−2$ are the two preceding terms.

The number $F15/5$ is the third term of the sequence given by,

$F15/5=F3=F2+F1=1+1=2$

Conclusion:

Thus, the value of $F15/5$ is 2.

Answer 43

Ch. 13 - Compute the value of each of the following. a. F15...Ch. 13 - Compute the value of each of the following. a. F16...Ch. 13 - Prob. 3E Ch. 13 - Compute the value of each of the following. a....Ch. 13 - Describe in words what each of the expressions...Ch. 13 - Prob. 6E Ch. 13 - Given that F36=14,930,352 and F37=24,157,817, a....Ch. 13 - Prob. 8E Ch. 13 - Given that F36=14,930,352 and F37=24,157,817,...Ch. 13 - Given that F32=2,178,309 and F33=3,524,578, a.find...

Compute the value of each of the following. a. F 15 b. F 15 − 2 c. F 15 − 2 d. F 1515 e. F 15 / 5

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Answer to Problem 1E

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Answer to Problem 1E

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Answer to Problem 1E

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Answer to Problem 1E

Explanation of Solution

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