Find the sum: (-5) + (-8) + (-11) + dots + (- | vedclass

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Question

(C) The given series is an Arithmetic Progression $(AP)$ where the first term $a = -5$ and the common difference $d = (-8) - (-5) = -3$.The last term

Vedclass · Accepted Answer

$-8930$

Vedclass · Answer

(C) The given series is an Arithmetic Progression $(AP)$ where the first term $a = -5$ and the common difference $d = (-8) - (-5) = -3$.The last term $l$ or $a_n = -230$.Using the formula for the $n^{th}$ term of an $AP$: $a_n = a + (n - 1)d$.$-230 = -5 + (n - 1)(-3)$.$-230 + 5 = (n - 1)(-3)$.$-225 = (n - 1)(-3)$.$n - 1 = \frac{-225}{-3} = 75$.$n = 76$.Now,using the sum formula $S_n = \frac{n}{2}(a + l)$:$S_{76} = \frac{76}{2}(-5 + (-230))$.$S_{76} = 38 	imes (-235)$.$S_{76} = -8930$.

Find the sum: $(-5) + (-8) + (-11) + \dots + (-230)$.

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