Question

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

Answer 1

We have,

It is given that,

$k^{th}term=5k+1$

Then,

$a_k=5k+1$

We know that the Sum of $nterms$,

Then,

$S_n=\frac{n}{2}[a+l]$

Last term will be this $=a_n=l$

Put $k=1$ and we get,

$a_1=5k+1$

$a_1=5\times 1+1$

$a_1=6$

Finding last term

Put $k=n$ in given,

$a_n=5n+1$

$l=5n+1$

Now,

$S_n=\frac{n}{2}(a+l)$

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

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

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

Hence, this is the answer.