Question

Find the sum of first $22$ terms of an A.P in which $d=22$ and $a_{22}=149$.

Answer 1

Given,

$22$nd term of A.P $a_{22}=149$

common difference $d=22$

number of terms $n=22$

we know that nth term of an A.P is given by

$a_n=a_1+(n-1)d$

hence 22nd term is given as

$a_{22}=a_1+(22-1)\times 22$

put $a_{22}=149$

$⟹149=a_1+21\times 22$

$⟹a_1+462=149$

$⟹a_1=149-462=-313$ first term of A.P

sum of n terms of an A.P is given by

$S_n=\frac{n}{2}(a_1+a_n)$

put $n=22;a_1=-313and{a}_{22}=149$

$⟹S_n=\frac{22}{2}(-313+149)$

$⟹S_n=11\times -164$

$⟹S_n=-1804$

hence sum of first $22$ terms of A.P is $-1804$