A sequence `{t_n}` is given by `t_n=n^2-1, n inN,` show that it is not an A.P.

A sequence { t_n} is given by t_n=n^2-1, n in N then show that it is not an A.P

The nth term of a sequence is given by a_(n)=2n^(2)+n+1. Show that it is not an A.P.

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

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 is S_(n) = n/2 (2a +(n-1)d)=n/2 (a+a+(n-1)d)= n/2 (a+l) A sequence whose n^(th) term is given by t_(n) = An + N , where A,B are constants , is an A.P with common difference

Show that the sequence t_(n) defined by t_(n)=(2^(2n-1))/(3) for all values of n in N is a GP. Also, find its common ratio.

Show that the sequence t_(n) defined by t_(n)=5n+4 is AP, also find its common difference.

Show thast the sequence (t_(n)) defined by t_(n)=x+(2n-1)b, wherex and b are constants,is an A.P.Fid its 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.

Show that the sequence given by T_(n)=(2xx3^(n)) for all n in N is a GP. Find its first term and the common ratio.