Find the sum of first n terms of the A.P. 6, | vedclass

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(A) The given $A.P.$ is $6, 2, -2, \ldots$Here,the first term $a = 6$ and the common difference $d = 2 - 6 = -4$.The sum of the first $n$ terms of an

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$2n(4-n)$

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(A) The given $A.P.$ is $6, 2, -2, \ldots$Here,the first term $a = 6$ and the common difference $d = 2 - 6 = -4$.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 $d$ into the formula:$S_{n} = \frac{n}{2} [2(6) + (n - 1)(-4)]$$S_{n} = \frac{n}{2} [12 - 4n + 4]$$S_{n} = \frac{n}{2} [16 - 4n]$$S_{n} = n(8 - 2n) = 8n - 2n^{2} = -2n^{2} + 8n$.

Find the sum of first $n$ terms of the $A.P.$ $6, 2, -2, \ldots$

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