Question

If the sum of $n$ terms of an A.P is$2n^2+5n$, then the $nth$ term will be:

• A. $4n+3$
• B. $4n+5$
• C. $4n+6$
• D. $4n+7$

Answer 1

The correct option is A

$4n+3$

Explanation for the correct option.

Sum of $n$ terms of AP $=S_{\mathrm{n}}=2{\mathrm{n}}^2+5\mathrm{n}$

$\begin{array}{rcl}& \Rightarrow & S_{\mathrm{n}-1}=2{\left(\mathrm{n}-1\right)}^2+5\left(\mathrm{n}-1\right)\\ & =& 2n^2-4n+2+5n-5\\ & =& 2n^2+n-3\end{array}$

The $nthterm=T_n=S_n-S_{n-1}$

$\begin{array}{rcl}& \Rightarrow & T_n=2n^2+5n-\left(2n^2+n-3\right)\\ & =& 4n+3\end{array}$

Hence, option A is correct.