If nth term of a sequences is `2n+b, where a,b` are constants, is the this sequence an A.P.?

If the sum to n terms of a sequences is 2n^(2)+4, find its nth.Is this seqwuence as AP?

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

If the nth term of a sequence is an expressionof first degree in n,show that it is an A.P.

If the sum to n terms of a sequence be n^(2)+2n then prove tht the sequence is an 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.

If sum of n terms of a sequence is S_n then its nth term t_n=S_n-S_(n-1) . This relation is valid for all ngt-1 provided S_0= 0. But if S_1=0 , then the relation is valid only 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 the following 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.

p : · If nth term of a sequence _is linear then sequence is in A.P. Converse of statement p is

Show that the sequence defined by a_(n) = m + (2n - 1) d, where m and d are constants , is an A.P. Find its common difference .

A sequence is called an A.P if the difference of a term and the previous term is always same i.e if a_(n+1)- a_(n)= constant ( common difference ) for all n in N For an A.P whose first term is 'a ' and common difference is d has n^(th) term as t_n=a+(n-1)d Sum of n terms of an A.P. whose first term is a, last term is l and common difference is d is S_(n) = n/2 (2a +(n-1)d)=n/2 (a+a+(n-1)d)= n/2 (a+l) If sum of n terms S_n for a sequence is given by S_n=An^2+Bn+C , then sequence is an A.P. whose common difference is

If nth term of an A.P. is (2n+1), what is the sum of its first three terms?