Prove that the sum of n terms of GP with first term a and common ratio r is given by `S_n=a(r^n-1)/(r-1)`

Prove that the nth term of the GP with first term a and common ratio r is given by a_(n)=ar^(n-1)

The sum of an infinite GP with first term a and common ratio r(-1

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

Show that sum S_(n) of n terms of an AP with first term a and common difference d is S_(n)=(n)/(2)(2a+(n-1)d)

Write three terms of the GP when the first term : a 'and the common ratio r are given a=4, r=3

Let S_n denote the sum of first n terms of a G.P. whose first term and common ratio are a and r respectively. On the basis of above information answer the following question: The sum of product of first n terms of the G.P. taken two at a time in (A) (r+1)/r S_nS_(n-1) (B) r/(r+1)S_n^2 (C) r/(r+1)S_nS_(n-1) (D) none of these

Let S_n denote the sum of first n terms of a G.P. whose first term and common ratio are a and r respectively. On the basis of above information answer the following question: S_1+S_2+S_2+..+S_n= (A) (na)/(1-r)-(ar(1-^n))/((1-r)^20 (B) (na)/(1-r)-(ar(1+^n))/((1+r)^20 (C) (na)/(1-r)-(a(1-^n))/((1-r)^20 (D) none of these

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))