Let `a_n = n^2 + 1 ` and `b_n` is defined `b_n = a_(n+1) -a_n`. Show that `{b_n}` is an arithmetic sequence.

A sequence {a_n} is given by : a_n=n^2-1, n in N . Show that it is not an A.P.

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

The nth term of a series is given by t_n = (n^5 + n^5)/(n^4 + n^2 + 1) and if sum of its n terms can be expressed as s_n = a_n^2 + a + 1/(b_n^2 + b) , where a_n and b_n are the nth terms of some arithmetic progression and a, b are some constants , then prove that b_n/a_n is a constant.

Let sequence by defined by a_1=3,a_n=3a_(n-1)+1 for all n >1

In the sequence a_n , then nth term is defined as (a_(n - 1) - 1)^2 . If a_(1) = 4 , then what is the value of a_2 ?

Find the sequence of the numbers defined by a_n={1/n , when n is odd -1/n , when n is even

Find the sequence of the numbers defined by a_n={1/n , when n is odd -1/n , when n is even

Let the sequence a_n be defined as a_1=1, a_n=a_(n-1)+2 for n ge 2 . Find first five terms and write corresponding series.

Show that the sequence defined by a_n=2/(3^n),\ n in N\ is a G.P.