The sum of n terms of a progression is `(2^(n)-1)`. Show that it is a GP and find its common ratio.

The nth term of a progression is 2^(n). Prove that it is G.P. Also find its common ratio.

The nth term of a progression is 2^(n). Prove that it is G.P. Also find its common ratio.

The nth term of a progression is 3^(n+1) . Show that it is a G.P. Also find its 5th term.

The nth term of a progression is 3^(n+1) . Show that it is a G.P. Also find its 5th term.

The sum of 'n' terms of a progression is (n^(2)+5n). Prove that it is arithmetic progression. Also find its common difference.

If the sum of the first n terms of a sequence is 2(7^(n)-1)//3 show that it is a G.P. Also , find its first term and common ratio.

The sum of n terms of an Arithmetic progression is S_n=2n^2+6n . Find the first term and the common difference.

If the sum of 'n' terms of an arithmetic progression is S_(n)=3n +2n^(2) then its common difference is :

The sum of n terms of two arithmetic progression is in the ratio 2n+1:2n-1. Find the ratio of 10^(t)h term.