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

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.

If the sum of n terms of an A.P. is (pn+qn^(2)), where p and q are constants, find the common difference.

Sum of first n terms of an A.P.is of the form An^(2)+Bn i.e.aquadratic expression in n, in such case the common differenceis twice the coefficient of n^(2). i.e.2A

(V)A Sequence is an AP ; if its nth term is linear expressions in n i.e.a_(n)=An+B where A and B are constants.In such a case the cofficients of n is a_(n) is the common difference of AP.

If the sum of n terms of an A.P.is (pn+qn^(2)) where p and q are constants,find the common difference.

If n^(th) term of A.P is 2n+3, then common difference is

If the sum of n terms of an A.P.is nP+(1)/(2)n(n-1)Q, where P and Q are constants,find the common difference.

If the sum of n terms of an AP is Pn+Qn^(2) where P,Q are constants,then its common differc