Question

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

Answer 1

Given $d=7,a_{22}=149$

We want to find $S_{22}.$

$a_n=a+(n-1)d$

$\Rightarrow a_{22}=a+(22-1)7$

$\Rightarrow 149=a+\left(21\right)\left(7\right)$

$\Rightarrow 149=a+147$

$\therefore a=2$

We have $S_n=\frac{n}{2}(a+a_n)$ then

$S_{22}=\frac{22}{2}(2+149)$

$=11\times 151$

$=1661$