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

Answers (1)

Sum of n terms of G.P. is given by = {a(rn - 1)}/(r - 1)
ATQ
{a(r8 - 1)}/(r - 1) = 5{a(r4 - 1)}/(r - 1)
(r4)2 - 1 = 5(r4 - 1)
(r4 + 1)(r4 - 1) = 5(r4 - 1)
r4+1 = 5
r2 = 2 0r -2 As square can't be neagtive
r2 = 2  
Common ratio r = √2 or -2

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