Prove that a sequence in an A.P., if the sum of its `n` terms is of the form `A n^2+B n ,w h e r eA ,B` are constants.

Write the n t h term of an A.P. the sum of whose n terms is S_n .

The nth term of an A.P. is (5n-1). Find the sum of its 'n' terms.

If the sum of first n terms of an A.P. is 3n^2 + 2n , find its r^(th) term.

If the n^(t h) term of an A.P. is (2n+1), find the sum of first n terms of the A.P.

In an A.P., the sum of first n terms is (3n^2)/2+(13)/2n . Find its 25 t h term.

In an A.P., the sum of first n terms is (3n^2)/2+(5n)/2dot Find its 25th term.

Write the common difference of an A.P. the sum of whose first \ \ n terms is P/2n^2+Q n

Find the rth term of an A.P., the sum of whose first n terms is 3n^2+4n

If the sum of first n terms of an A.P. is an^(2) + bn and n^(th) term is An + B then

(a) The sum of 'n' terms of a progression is n(n + 1). Prove that it is an A..P. Also find its 10th term. (b) The sum of 'n' terms of a progression is (3n^(2) - 5n). Prove that it is an A.P. (c) If the sum of n terms of a series is (5n^(2) + 3n) then find its first five terms.