Chapter 12.2, Problem 4AYU

True or False The sum $S_n$ of the first $n$ terms of an arithmetic sequence $\left\{a_n\right\}$ whose first term is $a_1$ can be found using the formula $S_n=\frac{n}{2}\left(a_1+a_n\right)$.

To determine

Check whether the given statement is true or false: The sum $S_n$ of the first $n$ terms of an arithmetic sequence $\left\{a_n\right\}$ whose first term is $a_1$ can be found using the formula $S_n=\frac{n}{2}\left(a_1+a_n\right)$.

Answer to Problem 4AYU

True.

Explanation of Solution

Given:

The sum $S_n$ of the first $n$ terms of an arithmetic sequence $\left\{a_n\right\}$ whose first term is $a_1$ can be found using the formula $S_n=\frac{n}{2}\left(a_1+a_n\right)$.

Calculation:

By the Theorem for Sum of the first $n$ terms of an arithmetic sequence, $a_1$ can be found using the formula $S_n=\frac{n}{2}\left(a_1+a_n\right)$.

Therefore, the above statement is true.