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# Find the sum to n terms of the A.P., whose k th term is 5k plus 1.

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

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Given : $a_k=5k+1$

$\Rightarrow \, \, a+(k-1)d=5k+1$

$\Rightarrow \, \, a+kd-d=5k+1$

Comparing LHS and RHS , we have

$a-d=1$        and     $d=5$

Putting value of d,

$a=1+5=6$

$S_n=\frac{n}{2}[2a+(n-1)d]$

$S_n=\frac{n}{2}[2(6)+(n-1)5]$

$S_n=\frac{n}{2}[12+5n-5]$

$S_n=\frac{n}{2}[7+5n]$

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