Question

Find the sum of first 32 terms of the arithmetic series if $a_1=12$ and $a_{32}=40$.

• A. $830$
• B. $831$
• C. $832$
• D. $834$

Answer 1

Answer: (C)

$832$

Given:
First term $=12$
last term $=40$

The sum of $n$ terms of arithmetic sequence can be calculated by the formula $S_n=\frac{n}{2}(a_1+a_n)$
Where $n$ is the number of terms, $a_1$ is the first term and $a_n$ is the last term.

Here, $n=32$

$\therefore S_{32}=\frac{32}{2}(12+40)$

$=16(12+40)$

$=16\left(52\right)$

$=832$

Hence, the sum of the first $32$ terms is $832$