Question

Find the sum of the AP: $2,5,8,11,\dots$ to first $11$ terms.

• A. $187$
• B. $178$
• C. $192$
• D. $171$

Answer 1

Answer: (A)

$187$

The sum of first $n$ terms of an AP whose first term is $a$ and common difference is $d$ is given by,

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

Here

$d=5-2$

$=3$

$a=2$

So,

$S_{11}=\frac{11}{2}[4+(11-1)\times 3]$

$=\frac{11}{2}[4+30]$

$=\frac{11}{2}\times 34$

$=11\times 17$

$=187$

Hence, option $A$ is correct.