Question

Find the sum of the following APs:
$-37,-33,-29,...$ to $12$ terms

Answer 1

$-37,-33,-29,...$ to $12$ terms are in AP
$a=-37$, $d=a_2-a_1=(-33)-(-37)=4$, $n=12$
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$S_{12}=\frac{12}{2}[2\times (-37)+(12-1\left)4\right]$
$=6[-74+(11\times 4\left)\right]$
$=6[-74+44]$
$=6[-30]$
$=-180$
$\therefore S_{12}=-180$