Question

If the sum of first n term of A.P is $\frac{1}{2}(3n^2+7n)$ then its $n^{t}h$ term. hence ${20}^{t}h$ term

Answer 1

First term, $a=S_1=\frac{1}{2}(3+7)=5$

Second term, $a+d=S_2-S_1=\frac{1}{2}(12+14)-\frac{1}{2}\left(10\right)=8\Rightarrow d=3$

$\Rightarrow a_n$($n^{th}$ term)$=a+(n-1)d=5+3(n-1)=3n+2$

$a_{20}=60+2=62$.