Question

In an infinite geometric progression,the sum of first two terms is 6 and every term is four times the sum of all the terms that follow it.find 1. The geometric progression 2.its sum to infinity. Plz help

Answer 1

Geometric series is    a,  a r , a r², ...    a = first term and common ratio is r

Tn = a r^(n-1)        Sn = a (1 - r^n) / (1-r)
Sum to infinity =  a / (1-r)        if r < 1

a + a r = 6        a ( 1 + r ) = 6      -- equation 1

a = 4 * [ a r + a r² + ... ] = 4 a r [ 1 + r + r² ..] = 4 a r / (1 -r )

SO,  1 - r = 4 r    => r = 0.2 or 1/5

a = 6/1.2 = 5

G. Progression is 5, 1/5, 1/25, ....

Sum to infinity: a / (1-r) = 5 / 0.8 = 6.25