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.

State 'T' for true and 'F' for false . I. A sequence is an A.P ., if and only if the sum of its n terms is of the form An^(2) +Bn , where A and B are constants . II. If 18, a, b , -3 are in A.P., then a+b = 15 . III If a,c,b are in A.P., then 2c=a+b . IV .The n^(th) term from the end of an A.P. is the (m-n+1)^(th) term from the beginning , where m terms are in A.P.

(vi)A sequence is an AP if the sum of its first n terms is of the form An^(2)+Bn where A and B are constants independent of n. In such a case the common difference is 2A

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

In an A.P., th e sum of its first n terms is 6n-n^(2). Find its 25 th term.

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

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

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

If the sum of n terms of an AP is n^2-2n then find its n^(th) term

If the sum of first n terms of an A.P. is 3n^(2)-2n , then its 19th term is

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