Find the sum to n terms of the A.P. whose k^{ | vedclass

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(A) The $k^{	ext{th}}$ term of the $A.P.$ is given by $a_k = 5k+1$.To find the first term $a_1$,substitute $k=1$:$a_1 = 5(1)+1 = 6$.To find the secon

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$\frac{n}{2}(5n+7)$

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(A) The $k^{	ext{th}}$ term of the $A.P.$ is given by $a_k = 5k+1$.To find the first term $a_1$,substitute $k=1$:$a_1 = 5(1)+1 = 6$.To find the second term $a_2$,substitute $k=2$:$a_2 = 5(2)+1 = 11$.The common difference $d$ is $a_2 - a_1 = 11 - 6 = 5$.The sum of $n$ terms of an $A.P.$ is given by $S_n = \frac{n}{2}[2a + (n-1)d]$.Substituting $a=6$ and $d=5$:$S_n = \frac{n}{2}[2(6) + (n-1)5]$$S_n = \frac{n}{2}[12 + 5n - 5]$$S_n = \frac{n}{2}[5n + 7]$.

Find the sum to $n$ terms of the $A.P.$ whose $k^{\text{th}}$ term is $5k+1$.

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