If the sum to n terms of a sequence be `n^2+2n` then prove that the sequence is an A.P.

The nth term of a sequence is 8 -5n. Show that the sequence is an A.P.

If sum of n termsof a sequende is S_n then its nth term t_n=S_n-S_(n-1) . This relation is vale for all ngt-1 provided S_0= 0. But if S_!=0 , then the relation is valid ony for nge2 and in hat cast t_1 can be obtained by the relation t_1=S_1. Also if nth term of a sequence t_1=S_n-S_(n-1) then sum of n term of the sequence can be obtained by putting n=1,2,3,.n and adding them. Thus sum_(n=1)^n t_n=S_n-S_0. if S_0=0, then sum_(n=1)^n t_n=S_n. On the basis of above information answer thefollowing questions: If the sum of n terms of a sequence is 10n^2+7n then the sequence is (A) an A.P. having common difference 20 (B) an A.P. having common difference 7 (C) an A.P. having common difference 27 (D) not an A.P.

If nth term of a sequences is 4n^2+1, find the sequence. Is this sequences at A.P.?

If the sum of n terms of an A.P. is 2n^2+3n then write its nth term.

If in an A.P. the sum of m terms is equal of n and the sum of n terms is equal to m , then prove that the sum of -(m+n) terms is (m+n) .

If the sum of n terms of a sequence is quadratic expression it always represents an AP.

If the sum of n terms of an A.P. is 2n^(2)+5n , then its n^(th) term

Find the sum to n terms of the sequence given by a_n=2^n,n in Ndot

If in an A.P. the sum of m terms is equal to n and the sum of n terms is equal to m then prove that the sum of (m+n) terms is -(m+n)

If the sum of n terms of a sequence is given by S_(n)=3n^(2)-2nAA n in N , then its 10th term is