Sum to n terms of a GP

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 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 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

If S_(n) denotes the sum fo n terms of a G.P. whose first term and common ratio are a and r respectively then show that: S_(1)+S_(3)+S_(5)+……..+S_(2n)-1=(an)/(1-r)-(ar(1-r^(2n)))/((1-r^(2))

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 GP.

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.

The ratio of the sum of 3 terms to the sum of 6 terms of a G.P. is 125:152. Its common ratio is :