Find the sum of n terms of the A.P.

Question:

Find the sum of n terms of the A.P. whose kth terms is 5k + 1.

Solution:

We have:

$a_{k}=5 k+1$

For $k=1, a_{1}=5 \times 1+1=6$

For $k=2, a_{2}=5 \times 2+1=11$

For $k=n, a_{n}=5 n+1$

$\therefore S_{n}=\frac{n}{2}\left[a+a_{n}\right]$

$\Rightarrow S_{n}=\frac{n}{2}[6+5 n+1]=\frac{n}{2}(5 n+7)$

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