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

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(A) The given series is $-5 + (-8) + (-11) + \ldots + (-230)$.This is an Arithmetic Progression $(A.P.)$ where the first term $a = -5$ and the last te

Vedclass · Accepted Answer

$-8930$

Vedclass · Answer

(A) The given series is $-5 + (-8) + (-11) + \ldots + (-230)$.This is an Arithmetic Progression $(A.P.)$ where the first term $a = -5$ and the last term $l = -230$.The common difference $d = a_2 - a_1 = (-8) - (-5) = -8 + 5 = -3$.Let $-230$ be the $n^{	ext{th}}$ term of this $A.P.$Using the formula $l = a + (n - 1)d$:$-230 = -5 + (n - 1)(-3)$$-230 + 5 = (n - 1)(-3)$$-225 = (n - 1)(-3)$$n - 1 = \frac{-225}{-3} = 75$$n = 76$.Now,the sum of $n$ terms is given by $S_n = \frac{n}{2}(a + l)$:$S_{76} = \frac{76}{2}(-5 + (-230))$$S_{76} = 38(-235)$$S_{76} = -8930$.

Find the sum given below: $-5 + (-8) + (-11) + \ldots + (-230)$

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