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

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Solution

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

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