A squae `(a_n)` is given by the formula `a_n = 10 -3n`. Prove that it is an A.P.

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

If m times the mth term is equal to n times the nth term of an A.P. prove that(m+n)th term of an A.P. is zero.

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

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

Find the sum S_n of the cubes of the first n terms of an A.P. and show that the sum of first n terms of the A.P. is a factor of S_n .

In an AP :- given a = 5, d = 3, a_n = 50 find n and S_n .

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

Find the first five terms of the sequence whose n^(th) term is a_n = n/4

If a_1, a_2, a_3 ......a_n (n>= 2) are real and (n-1) a_1^2 -2na_2 < 0 then prove that at least two roots of the equation x^n+a_1 x^(n-1) +a_2 x^(n-2) +......+a_n = 0 are imaginary.

Find the first five terms of the following sequence whose n^(th) term is a_n = 5n + 3