Sum the series 51 + 50 + 49 + ldots + 21. | vedclass

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(A) The given series is an arithmetic progression where the first term $a = 51$,the common difference $d = -1$,and the last term $a_n = 21$.Using the

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$1116$

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(A) The given series is an arithmetic progression where the first term $a = 51$,the common difference $d = -1$,and the last term $a_n = 21$.Using the formula for the $n^{th}$ term of an arithmetic progression: $a_n = a + (n - 1)d$.Substituting the values: $21 = 51 + (n - 1)(-1)$.$21 = 51 - n + 1$.$21 = 52 - n$.$n = 52 - 21 = 31$.Now,using the sum formula $S_n = \frac{n}{2}(a + a_n)$:$S_{31} = \frac{31}{2}(51 + 21)$.$S_{31} = \frac{31}{2}(72)$.$S_{31} = 31 	imes 36 = 1116$.

Sum the series $51 + 50 + 49 + \ldots + 21$.

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