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

If the 12th term of an A.P. is -13 and the sum of the first four terms is 24, what is the sum of the first 10 terms ?

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

If mth term of an AP is 1/n and its nth term is 1/m , then show that its (mn)th term is 1

The first term of an A.P. is a, the second term is b and last term is c. Show that the sum of A.P. is : ((b+c-2a)(c+a))/(2(b-a)) .

Find the first six terms of the sequence whose first term is 1 and whose (n+1)th term is obtained by adding n to the nth term.

If the sum of the first n terms of a sequence is of the form An^2+ Bn , where A, B are constants independent of n, show that the sequence is an A.P. Is the converse true ? Justify your answer.

In an A.P., of which a is the first term, if the sum of the first p terms is zero, show that the sum of the next q terms is (-a(p +q)q)/(p-1) .

The nth term of an AP is 5-6n.Find a and d.