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

The n^(th) term of a sequence is given by T_n = 2n + 7. Show that it is an A.P. Also, find its 7^(th) term.

The sequence a(n) is defined by : a(n) =(n-1)(n- 2) (n -3). Show that the first three terms of the sequence are zero, but the rest of the terms are positive.

If the sum of n terms of an A.P. is given by delta_n=3n+2n^2 , then the common difference of an A.P. is

In an AP :- given a = 8, a_n = 62. S_n =210, find n and d .

In an AP :- given a_n = 4, d=2, S_n =-14, find n and a .

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

The ratio of the sums of m and n terms of an A.P. is m^2: n^2 . Show that the ratio of m^(th) and n^(th) term is (2m - 1 ) : (2n -1).

Determine an A.P. whose nth term is a_n=3n^2+5n .

Show that a_1,a_2,….a_n,… form an AP where an is defined as below,- a_n=3+4n Also find the sum of the first 15 terms in each case.

Show that a_1,a_2,….a_n,… form an AP where an is defined as below,- a_n=9-5n Also find the sum of the first 15 terms in each case.