Question

Find the first two terms of the sequence for which $S_n$ is given. $S_n=n^2(n+3)$.

Answer 1

$S_n=n^2(n+3)$

First term $=T_1=S_1=1^2(1+3)=4$

let $T_2$ be the second term

So $S_2=T_1+T_2=2^2(2+3)=20$

$\therefore T_2=20-T_1=20-4=16$

Hence first two terms of above sequence are 4 and 16

Note: $T_n=S_n-S_{n-1}$