Question

Find $n^{th}$ term of the series

$3\times 1^2,5\times 2^2,7\times 3^2,.....$

Answer 1

$3+1^2,5\times 2^2,7\times 3^2,.......$

Separate it as

$3,5,7,....$

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

$=3+2n-2\to (2n+1)$

$1^2,2^2,3^2....$

$\Rightarrow n^2$

So $n^{th}$ term will be

$(2n+1)n^2$.