Question

The sum of the first n terms of an A.P. is $2n^2+5n$. Then its nth term is :

• A. 4n + 3
• B. 4n - 3
• C. 3n - 4
• D. 3n + 4

Answer 1

The correct option is A 4n + 3

Let $S_n=2n^2+5n=\sum T_n$

$\sum T_n=2n^2+2n+3n$

$=2n(n+1)+3n$

$=4\frac{n(n+1)}{2}+3n$

$=4\sum n+3\sum 1$

$=\sum (4n+3)$

$\therefore T_n=4n+3$