`l, m, n` are three numbers in G.P., `a` is the first term of an A.P., whose `l th, mth` and `nth` terms are in H.P. If d is the common difference of the A.P.. prove that `a = (m + 1)d.`

If the mth term of an A.P is n and nth term is m , then pth term =

The mth term of an A.P. is n and nth term is m. Then rth term of it is

Sum of first n terms of an A.P. whose last term is l and common difference is d, is

In an A.P.,the first term is 22, nth term is -11 and the sum to first n terms is 66. Find n and d, the common difference.

What is the sum of first n terms of an A.P. whose first term is 'a' and common difference is 'd'?

The sum of first ten terms of an A.P. is 155 and the sum of first two terms of a G.P. is 9. The first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to the common difference of the A.P. Find the two progressions.

The sum of first ten terms of an A.P. is 155 and the sum of first two terms of a G.P. is 9. The first term of the A.P. is equal to the common ratio of the G.P., and the first term of the G.P. is equal to the common difference of the A.P. Find the two progressions.