Find the sum of the first 25 terms of the A.P | vedclass

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(D) The given $A.P.$ is $30, 26, 22, \ldots$Here,the first term $a = 30$ and the common difference $d = 26 - 30 = -4$.The number of terms $n = 25$.The

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$-450$

Vedclass · Answer

(D) The given $A.P.$ is $30, 26, 22, \ldots$Here,the first term $a = 30$ and the common difference $d = 26 - 30 = -4$.The number of terms $n = 25$.The formula for the sum of the first $n$ terms of an $A.P.$ is $S_n = \frac{n}{2} [2a + (n - 1)d]$.Substituting the values: $S_{25} = \frac{25}{2} [2(30) + (25 - 1)(-4)]$.$S_{25} = \frac{25}{2} [60 + (24)(-4)]$.$S_{25} = \frac{25}{2} [60 - 96]$.$S_{25} = \frac{25}{2} [-36]$.$S_{25} = 25 	imes (-18) = -450$.Thus,the sum of the first $25$ terms is $-450$.

Find the sum of the first $25$ terms of the $A.P.$ $30, 26, 22, \ldots$

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