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

(i) The nth term of a progression is 2n+1. Prove that it is an A. P. Also find its 5th term. (ii) The nth term of a progression is linear expansion in 'n' . Show that it is an A.P. (iii) The nth term of a progression is (n^(2)+1) . Show that it is not an A.P.

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 (2^(n)-1) . Show that it is a GP and find its common ratio.

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 2n+3. Show that it is an A.P. Also find is 10th term.

The nth term of a progression is 2n+3. Show that it is an A.P. Also find is 10th term.

(a) The nth term of a progression is (3n + 5) . Prove that this progression is an arithmetic progression. Also find its 6th term. (b) The nth term of a progression is (3 - 4n) . Prove that this progression is an arithmetic progression. Also find its common difference. (c) The nth term of a progression is (n^(2) - n + 1). Prove that it is not an A.P.

(a) The nth term of a progression is (3n + 5) . Prove that this progression is an arithmetic progression. Also find its 6th term. (b) The nth term of a progression is (3 - 4n) . Prove that this progression is an arithmetic progression. Also find its common difference. (c) The nth term of a progression is (n^(2) - n + 1). Prove that it is not an A.P.

If the nth term of a progression is (4n-10) show that it is an AP. Find its (i) first term, (ii) common difference, and (iii) 16th term.