Find the sum of the following APs -37, -33, - | vedclass

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Question

(D) The given $AP$ is $-37, -33, -29, \ldots$ up to $12$ terms.For this $AP$:First term $a = -37$Common difference $d = a_{2} - a_{1} = (-33) - (-37)

Vedclass · Accepted Answer

$-180$

Vedclass · Answer

(D) The given $AP$ is $-37, -33, -29, \ldots$ up to $12$ terms.For this $AP$:First term $a = -37$Common difference $d = a_{2} - a_{1} = (-33) - (-37) = -33 + 37 = 4$Number of terms $n = 12$We use the formula for the sum of $n$ terms of an $AP$:$S_{n} = \frac{n}{2} [2a + (n - 1)d]$Substituting the values:$S_{12} = \frac{12}{2} [2(-37) + (12 - 1)4]$$S_{12} = 6 [-74 + 11 	imes 4]$$S_{12} = 6 [-74 + 44]$$S_{12} = 6 (-30)$$S_{12} = -180$Thus,the sum of the first $12$ terms is $-180$.

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

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