Question

Find the AP whose sum to n terms is 2 $n^2$ + n.

Answer 1

Here, $S_n$ = 2 $n^2$ + n (Given)

Put n = 1, 2, 3, 4... in succession, we get

$S_1$=2($1^2$)+1=2+1=3

$S_2$ = 2($2^2$) + 2 = 8 + 2 = 10

$S_3$ = 2($3^2$) + 3 = 18 + 3 = 21

$S_4$ = 2($4^2$) + 4 = 32 + 4 = 36
and so on. $a_1$ = $S_1$ = 3

$a_2$ = $S_2$ - $S_1$ = 10 -3 = 7

$a_3$ = $S_3$ - $S_2$ = 21 -10 = 11

$a_4$ = 54 - $S_3$ = 36 -21 = 15

and so on.

Hence, the required AP is 3, 7, 11, 15...