Find the sum given below: 34 + 32 + 30 + ldot | vedclass

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(D) The given series is $34 + 32 + 30 + \ldots + 10$.This is an Arithmetic Progression $(A.P.)$ where the first term $a = 34$,the common difference $d

Vedclass · Accepted Answer

$286$

Vedclass · Answer

(D) The given series is $34 + 32 + 30 + \ldots + 10$.This is an Arithmetic Progression $(A.P.)$ where the first term $a = 34$,the common difference $d = 32 - 34 = -2$,and the last term $l = 10$.Let $n$ be the number of terms. The formula for the $n^{	ext{th}}$ term is $l = a + (n - 1)d$.Substituting the values: $10 = 34 + (n - 1)(-2)$.$10 - 34 = (n - 1)(-2) \implies -24 = (n - 1)(-2)$.Dividing by $-2$: $12 = n - 1 \implies n = 13$.The sum of $n$ terms is given by $S_n = \frac{n}{2}(a + l)$.$S_{13} = \frac{13}{2}(34 + 10) = \frac{13}{2}(44) = 13 	imes 22 = 286$.

Find the sum given below: $34 + 32 + 30 + \ldots + 10$

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