The sum of some terms of GP. is 315 whose first term and the common ratio are 5 and 2 respectively. Find the last term and the number of terms.

The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

Find the nth term of GP if the first term is 7 and common ratio is 3.

Find the 5th term of GP if the first term is 4 and common ratio is 2.

The first term of an A.P. is 5, the common difference is 3 and the last term is 80, find the number of terms.

Find the 7th term of GP if the first term is 7 and common ratio is 2.

The fourth, seventh, and the last term of a G.P. are 10, 80, and 2560, respectively. Find the first term and the number of terms in G.P.

Find the 10th term of a G.P. whose 8th term is 192 and the common ratio is 2.

Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.

The 2nd, 31st and last terms of an A.P. are 7 3/4, 1/2 and -6 1/2 respectively, find the first term and the number of terms.

If S_n represents the sum of n terms of a G.P. whose first term and common ratio are a and r respectively. Prove that : S_1 +S_2+S_3+.....+S_(m)= (am)/(1-r)-(ar(1-r^(m)))/((1-r)^2) .