Question

If the first term of an g.p.is is729and the seventh term is64 ,then sum of infinity

Answer 1

First term of G.P = 729
7th term of G.P = 64 .

we know,
nth term for G.P =a.r^(n-1)
where a is First term and r is common ratio.

7th term = a.r^(7-1)
64 = 729 r^6
(2)^6 =(3)^6 r^6
r^6 = (2/3)^6
r = 2/3

we know,
sum of infinity in G.P = a/(1 - r)
where 0 < r < 1
here r = 2/3
0 < 2/3 < 1
hence,
sum of infinity = 729/(1 - 2/3)
= 729/(1/3)
= 2187