Find the sum:1+(-2)+(-5)+(-8)+ldots+(-236) | vedclass

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(B) The given series is an Arithmetic Progression $(AP)$ where the first term $a = 1$ and the common difference $d = -2 - 1 = -3$.The last term is $l

Vedclass · Accepted Answer

$-9400$

Vedclass · Answer

(B) The given series is an Arithmetic Progression $(AP)$ where the first term $a = 1$ and the common difference $d = -2 - 1 = -3$.The last term is $l = a_n = -236$.Using the formula for the $n^{th}$ term of an $AP$: $a_n = a + (n - 1)d$.$-236 = 1 + (n - 1)(-3)$$-237 = (n - 1)(-3)$$n - 1 = 79$$n = 80$.Now,the sum of $n$ terms of an $AP$ is given by $S_n = \frac{n}{2}(a + l)$.$S_{80} = \frac{80}{2}(1 + (-236))$$S_{80} = 40 	imes (-235)$$S_{80} = -9400$.

Find the sum:
$1+(-2)+(-5)+(-8)+\ldots+(-236)$

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Find the sum:$1+(-2)+(-5)+(-8)+\ldots+(-236)$