Question

Find the sum of the first $p$ terms of the series whose $n^{th}$ term is $3n-1$.

Answer 1

As given $n^{th}$ term is $3n-1$

i.e. $t_n=3n-1$

By putting $n=1$ and $n=p$ respectively, we obtain
First term $t_1=2$ and last term $t_p=3p-1$;
$\therefore sum=\frac{p}{2}(2+3p-1)=\frac{p}{2}(3p+1)$.