Question

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

• A. $10n-2$
• B. $10n-3$
• C. $10n-4$
• D. $10n-6$

Answer 1

The correct option is A $10n-2$

Given, $S_n=5n^2+3n$
$\therefore S_{n-1}=5(n-1{)}^2+3(n-1)=5(n^2-2n+1)+3n-3$
$\Rightarrow S_{n-1}=5n^2-10n+5+3n-3=5n^2-7n+2$
Now, nth term $a_n=S_n-S_{n-1}$
$\Rightarrow a_n=(5n^2+3n)-(5n^2-7n+2)$
$\Rightarrow a_n=10n-2$