Question

 

The sum of first eight terms of a G.P. is five times the sum
of the first four terms.

Find the common ratio.

Answer 1

sum of n terms of G.P. is  = {a(r^n - 1)}/(r - 1)
  according to question ;
{a(r^8 - 1)}/(r - 1) = 5{a(r^4 - 1)}/(r - 1)
(r^4)^2 - 1 = 5(r^4 - 1)
r^4 + 1 = 5
r^4 = 4
r^2 = +2  or -2
r^2 = 2
r = +2^1/2  ,or -2^1/2
r^2  = -2     square of any number can not be negative ,hence
r = 2^1/2  or  -2^1/2    (r = common ratio)

Answer 2

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