Chapter 9, Problem 1E

Consider the sequence defined by the explicit formula $A_N=N^2+1$.

a. Find $A_1$.

b. Find $A_{100}$.

c. Suppose $A_N=10$. Find N.

To determine

(a)

To find:

The specified value of $A_1$ from the given sequence.

Answer to Problem 1E

Solution:

The value of $A_1$ is 2.

Explanation of Solution

Given:

The sequence with an explicit formula $A_N=N^2+1$.

Calculation:

The given sequence is $A_N=N^2+1$.

To obtain $A_1$ substitute 1 for $N$ in the above formula.

$\begin{array}{rll}{A}_1& =& 1^2+1\\ & =& 2\end{array}$

Therefore, the value of $A_1$ is 2.

Conclusion:

The value of $A_1$ is 2.

To determine

(b)

To find:

The specified value of $A_{100}$ from the given sequence.

Answer to Problem 1E

Solution:

The value of $A_{100}$ is 10001.

Explanation of Solution

Given:

The sequence with an explicit formula $A_N=N^2+1$.

Calculation:

The given sequence is $A_N=N^2+1$.

To obtain $A_{100}$ substitute 100 for $N$ in the above formula.

$\begin{array}{rll}{A}_{100}& =& {100}^2+1\\ & =& 10001\end{array}$

Therefore, the value of $A_{100}$ is 10001.

Conclusion:

The value of $A_{100}$ is 10001.

To determine

(c)

To find:

The value of $N$ for the given value of $A_N$.

Answer to Problem 1E

Solution:

The value of $N$ is 3.

Explanation of Solution

Given:

The sequence with an explicit formula $A_N=N^2+1$.

The given value of $A_N$ is 10.

Calculation:

The given sequence is $A_N=N^2+1$.

Substitute 10 for $A_N$ in the above formula.

$\begin{array}{rll}10& =& N^2+1\\ N^2& =& 10-1\\ N& =& \sqrt{9}\\ & =& 3\end{array}$

Therefore, the value of $N$ is 3.

Conclusion:

The value of $N$ is 3.