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

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Question

(A) The given $A.P.$ is $5, 2, -1, \ldots$Here,the first term $a = 5$.The common difference $d = 2 - 5 = -3$.The sum of the first $n$ terms of an $A.P

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$S_n = -\frac{3}{2}n^2 + \frac{13}{2}n$

Vedclass · Answer

(A) The given $A.P.$ is $5, 2, -1, \ldots$Here,the first term $a = 5$.The common difference $d = 2 - 5 = -3$.The sum of the first $n$ terms of an $A.P.$ is given by the formula $S_n = \frac{n}{2}[2a + (n - 1)d]$.Substituting the values of $a$ and $d$:$S_n = \frac{n}{2}[2(5) + (n - 1)(-3)]$$S_n = \frac{n}{2}[10 - 3n + 3]$$S_n = \frac{n}{2}[13 - 3n]$$S_n = \frac{13n}{2} - \frac{3n^2}{2}$Thus,$S_n = -\frac{3}{2}n^2 + \frac{13}{2}n$.

Find the sum of the first $n$ terms of the $A.P.$ $5, 2, -1, \ldots$

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