Define an arithmetic progression.

(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.

Let {a _(1),a _(2), a _(3)......} be a strictly increasing sequence of positive integers in an arithmetic progression. Prove that there is an infinite subsequence of the given sequence whose terms are in a geometric progression.

The sum of three numbers m GP is 56. If we subtract 1.7,21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.