Question

If $S_n$, the sum of first $n$ terms of an A.P., is given by $S_n=5n^2+3n$, then find its $n^{th}$ term.

Answer 1

Let $a_n$ be the $n^{th}$ term of the A.P.

Then, $a_n=S_n-S_{n-1}$

$⟹a_n=(5n^2+3n)-\left\{5\right(n-1{)}^2+3(n-1)\}$

.......... $\left[Replacingnby\right(n-1)in{S}_{n}toget{S}_{n-1}=5(n-1{)}^2+3(n-1)]$

$⟹a_n=(5n^2+3n)-(5n^2-7n+2)$

$⟹a_n=10n-2$