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.

Prove that a sequence in an A.P.if the sum of its n terms is of the form An^(2)+Bn, where A,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

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

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.

If the sum of the first n terms of a sequence is of the form An^2+ Bn , where A, B are constants independent of n, show that the sequence is an A.P. Is the converse true ? Justify your answer.

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

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