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

$\begin{array}{1 1} =\large\frac{n(5n+1)}{2} \\=\large\frac{n(5n+6)}{2} \\=\large\frac{n(5n-7)}{2} \\ =\large\frac{n(5n+7)}{2} \end{array}$

Toolbox:
• Sum of $n$ terms of an $A.P.=\large\frac{n}{2}$$[l+a] where a= first term and l=last term=t_n Given: k^{th} term t_k=5k+1 \therefore\:t_n=5n+1 \therefore\:t_1=a\:(first\:term)=5+1=6 We know that s_n=\large\frac{n}{2}$$(l+a)$
$\therefore\:S_n=\large\frac{n}{2}$$(t_n+6)=\large\frac{n}{2}$$(5n+1+6)$
$=\large\frac{n(5n+7)}{2}$