If the sum of it terms of an A.P. is 2n2 + 5n, then its nth term is

Answer: Option C

Let a be the first term and d be the common difference of an A.P. and
$$\begin{array}{rl}& S_n=2n^2+5n\\ & \therefore S_1=2{\left(1\right)}^2+5\times 1\\ & =2+5\\ & =7\\ & \therefore S_2=2{\left(2\right)}^2+5\times 2\\ & =8+10\\ & =18\\ & \therefore \text{First}\text{term}\left(a_1\right)=7\text{and}\\ & \text{Second}\text{term}{a}_2=S_2-S_1\\ & =18-7\\ & =11\\ & \therefore d=a_2-d_1\\ & =11-7\\ & =4\\ & Now{a}_n=a+\left(n-1\right)d\\ & =7+\left(n-1\right)4\\ & =7+4n-4\\ & =4n+3\end{array}$$