For a sequence, if `S_n = 7 (4^n - 1)`, find the `t_n` and show that the sequence is a G.P.

For a sequence, if S_n = 2(3^n - 1) , find the term, hence show that sequence is a G.P.

If for a sequence (t_n) , S_n = 2n^2 + 5 , find t_n and show that the sequence is an A.P.

For a sequence, if S_n = (4^n - 3^n) / 3^n , find the nth term. Hence show that it is a G.P. Also find the common ratio.

For a sequence, if S_n = 3(2^n - 1) , find the nth term. Hence show that it a G.P. Also find the common ratio.

If for a sequence, t_n = 2^(n - 1) / 5^(n - 1) , show that the sequence is a G.P. Find its first term and common ratio.

For a sequence , if Sn = 5(4^(n) -1), find the n^(th) term, hence verify that it is a G.P., Also find r.

If for a sequence, t_n = (-5)^(n+1) / 3^(n - 1) , show that the sequence is a G.P. Find its first term and common ratio.