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

The fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sum of its first eight terms.

If S₁, S₂, S₃ be respectively the sums of n, 2n, 3n terms of a G.P., then prove that S₁² + S₂² = S₁(S₂ + S₃)

_{Question May be wrong.}

If a and b are the roots of x² – 3x + p = 0 and c, d are the roots x² – 12x + q = 0, where a, b, c, d form a G.P. Prove that (q + p) : (q – p) = 17 : 15.

How many terms of the G.P. are needed to give the sum ?