Prove that the product of first 'n' terms of a G.P., whose first term is ‘a’ and last term is` ‘l’ `, is `(al)^(n/2)`.

Find the sum of first n terms of an A.P. whose nth term is 3n+1.

Find the arithmetic series of n terms whose first term is a and last term is l.

Find S_oo of G.P. whose first term is 28 and the fourth term is 4/49 .

Find the sum of the first a terms of the series whose nth term is: 3n^2+5 .

If ‘S’ is the sum of a finite A.P. whose first term is ‘a’ and last term is ‘l’, show that its common difference is equal to (l^2-a^2)/(2S-a-l) .

Find the sum of the first a terms of the series whose nth term is: n(n + 3) .

If S_n denotes the sum of n terms of an A.P. whose first term is a, and the common difference is d Find: = Sn - 2Sn + S(n +2) .

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n+ 1)th to (2n)th term is 1/r^n .

The sum of n terms of an A.P. whose first term is 5 and common difference is 36 is equal to the sum of 2n terms of another A.P. whose first term is 36 and common difference is 5. Find n.

If the sum of first n terms of an A.P. is cn^(2) then the sum of squares of these n terms is