Question

find the sum of first 22 terms of an AP in which d is 7 and 22nd term is 149.​

Answer 1

1661 is the answer

refer the following attachment for Step-by-step explanation

Answer 2

Given :-

• common difference (d) = 7

• 22nd term = 149

• n = 22

To find :-

• The sum of 22 terms of an AP.

Solution :-

$\rm\:a_{22}=149$

$\rm\longrightarrow\:a+21d=149$

$\rm\longrightarrow\:a+21\times{7}=149$

$\rm\longrightarrow\:a+147=149$

$\rm\longrightarrow\:a=149-147$

$\rm\longrightarrow\:a=2$

Now,

By using formula of Sn,

$\blue{\bigstar}\:\:{\underline{\boxed{\bf\red{s_n=\dfrac{n}{2}\:[2a+(n-1)d]}}}}$

$\rm\longrightarrow\:s_{22}=\dfrac{22}{2}\:[2\times{2}+(22-1)\times{7}$

$\rm\longrightarrow\:s_{22}=11(4+21\times{7})$

$\rm\longrightarrow\:s_{22}=11(4+147)$

$\rm\longrightarrow\:s_{22}=11\times{151}$

$\rm\longrightarrow\:s_{22}=1661$

Hence,the sum of first 22nd terms of an AP will be 1661