Sum to N terms Of An G.P

The sum of first three terms of a G.P is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.

The 1^st, 2^nd and 3^rd terms of an arithmetic series are a, b and a^2 where 'a' is negative. The 1^st, 2^nd and 3^rd terms of a geometric series are a, a^2 and b find the (a) value of a and b (b) sum of infinite geometric series if it exists. If no then find the sum to n terms of the G.P. (c) sum of the 40 term of the arithmetic series.

The common ratio, last term and sum of n terms of a G.P. are 2, 128 and 255 respectively. Find the value of n.

If the sum of n terms of a G.P.is 3-(3^(n+1))/(4^(2n)) then find the common ratio.

The 4 th and 7 th terms of a G.P.are (1)/(27) and (1)/(729) respectively.Find the sum of n terms of the G.P.

If S_(n) denotes the sum of n terms of a G.P., prove that: (S_(10)-S_(20))^(2)=S_(10)(S_(30)-S_(20))

If the sum of n terms of a G.P. (with common ratio r) beginning with the p^(th) term is k times the sum of an equal number of terms of the same series beginning with the q^(th) term, then the value of k is.

if S_(n) denotes the sum of n terms of a G.P whose first term is a and common ratio is r then find the sum of S_(1),S_(3),S_(5).........,S_(2)n-1