Question

Find the sum of first 22 terms of an AP in which d = 7 and the 22${}^{nd}$ term is 149.

• A. 1661
• B. 1542
• C. 1712
• D. 1623

Answer 1

The correct option is A

1661

It is given that 22${}^{nd}$ term is equal to 149.

It means $a_{22}=149$

Using formula $a_n=a+(n-1)d$, to find $n^{th}$ term of AP, we can say that

$149=a+(22-1)7$

$\Rightarrow 149=a+147$

$\Rightarrow a=2$

Applying formula, $S_n=\frac{n}{2}(2a+(n-1\left)d\right)$ to find Sum of n terms of AP and putting value of a, we get

$S_{22}=\frac{22}{2}(4+(22-1\left)7\right)$

$\Rightarrow S_{22}=11(4+147)$

$\Rightarrow S_{22}=1661$

Therefore, sum of first 22 terms of the AP is equal to 1661.