`t_n = n^3 -3` , find series

If the sum of first n terms of a series is 2n^(2) + 3n , find the series.

In the series, T_n = 2n + 5 , find S_4 .

For the series sum t_(n,) S_n=sum_(n=1)^nt_n=2t_n-1 . Is the series geometric ? If so, find the sum to n terms of the series.

The sum of n terms of a series is 2n^2+3n . Is the series arithmetic ? If so, find it.

If t_(n)=an^(-1) , then find the value of n, given that a=2,r=3 and t_(n)=486 .

Find the sum of the following series whose n t h term is: 2n^3+3n^2-1.

Find the sum of the following series whose n t h term is: 2n^3+3n^2-1.

Let the n^(th) term of a series be given by t_n = (n^2 -n-2)/(n^2+3n),n leq 3 . Then product t_3 t_4 .....t_50 is equal to