Chapter 4.7, Problem 1P

a.

To determine

To find : the next two germs of each sequence.

Answer to Problem 1P

29 and 35

Explanation of Solution

Given sequence: $5,11,17,23,\mathrm{.....}$

Calculation:

Since the each term of given sequence after the first term is obtained by adding the previous one by 6, therefore given sequence is an arithmetic sequence.

Therefore, the next two terms of the sequence are

  $\begin{array}{l}23+6=29\\ 29+6=35\end{array}$

Thus, the next two terms of the sequence are 29 and 35.

b

To determine

To find : a recursive formula that represents the same sequence..

Answer to Problem 1P

25 and 12.5

Explanation of Solution

Given sequence: $400,200,100,50,\mathrm{.....}$

Calculation:

Since the each term of given sequence after the first term is obtained by multiplying the previous one by $\frac{1}{2}$ , therefore given sequence is a geometric sequence.

Therefore, the next two terms of the sequence are

  $\begin{array}{l}50\times \frac{1}{2}=25\\ 25\times \frac{1}{2}=12.5\end{array}$

Thus, the next two terms of the sequence are 25 and 12.5

c.

To determine

To find : the next two germs of each sequence.

Answer to Problem 1P

32 and $-64$

Explanation of Solution

Given sequence: $2,-4,8,-16,\mathrm{.....}$

Calculation:

Since the each term of given sequence after the first term is obtained by multiplying the previous one by $-2$ , therefore given sequence is a geometric sequence.

Therefore, the next two terms of the sequence are

  $\begin{array}{l}-16\times \left(-2\right)=32\\ 32\times \left(-2\right)=-64\end{array}$

Thus, the next two terms of the sequence are 32 and $-64$ .

d

To determine

To find : a recursive formula that represents the same sequence..

Answer to Problem 1P

1 and 5

Explanation of Solution

Given sequence: $-15,-11,-7,-3,\mathrm{.....}$

Calculation:

Since the each term of given sequence after the first term is obtained by adding the previous one by 4, therefore given sequence is an arithmetic sequence.

Therefore, the next two terms of the sequence are

  $\begin{array}{l}-3+4=1\\ 1+4=5\end{array}$

Thus, the next two terms of the sequence are 1 and 5.