Question

If the sum of n terms of an A.P. is 2 n² + 5 n, then its nth term is
(a) 4n − 3
(b) 3 n − 4
(c) 4 n + 3
(d) 3 n + 4

Answer 1

(c) 4 n + 3

$$\begin{gathered} S_n=2n^2+5n \\ {S}_1=2.1^2+5.1=7 \\ \therefore a_1=7 \\ {S}_n=2.2^2+5.2=18 \\ \therefore a_1+a_2=18 \\ \Rightarrow a_2=11 \\ \mathrm{Common}\mathrm{difference},d=11-7=4 \\ {a}_n=a+\left(n-1\right)d \\ =7+\left(n-1\right)4 \\ =4n+3 \end{gathered}$$