Question

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

Answer 1

$d = 7$, $a_{22} = 149$, $S_{22 }=?$
$a_n = a + (n − 1)d$
$a_{22} = a + (22 − 1)d$
$149 = a + 21 × 7$
$149 = a + 147$
$a = 2$
$S_n = \frac n2[a + a_n]$

$S_{22} = \frac {22}{2 }[2 + 149]$
$S_{22}= 11 \times 151$
$S_{22}= 1661$