The ratio of sum of first three terms is to that of first six term of a G.P is 125:152.find common ratio

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The ratio of sum of first three terms is to that of first six term of a G.P is 125:152.find common ratio

Anurag kumar 5th Apr, 2018

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Answer (1)

Dhanani Brijesh Rajeshbhai 9th Jun, 2018

Hello dear,

i have listed below all the calculation check it.

formula for sum of nth term in GP (Sn)= a(rⁿ -1)/(r -1)
according to the question,
S3/S6 = 125/152
{a(r³ - 1)/(r -1)}/{a(r^6 -1)/(r -1)} = 125/152
(r³ -1)/(r³ -1)(r³+1) = 125/152
1/(r³ + 1) = 125/152
152 = 125r³ + 125
27 =125r³
27/125 = r³
(3/5)³ = r³
ratio = 3/5

Hope This Helps.

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