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

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)

Find the nth term of GP if the first term is 7 and common ratio is 3.

Write the terms of the G.P. When the first term 'a' and the common ratio 'r' are given. a = 16, r= -1/2

Write the terms of the G.P. When the first term 'a' and the common ratio 'r' are given. a = sqrt3 , r=1/2

Write three terms of G.P. when the first term 'a' and the common ratio 'r' are given. r = -13 and a =1

If a_n is the n^(th) term of an A.P whose first term is a and common difference is d, prove that n=(a_n-a)/d+1

If S_n represents the sum of n terms of a G.P. whose first term and common ratio are a and r respectively. Prove that : S_1 +S_2+S_3+.....+S_(m)= (am)/(1-r)-(ar(1-r^(m)))/((1-r)^2) .

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))

If the n^(th) term of a G.P. is 3 (4^(n+1)) then its first term and common ratio are respectively