Discussion
The sum of first three terms of a G.P. is to the sum of first six terms as 125:152. Find the common ratio.
Answer: B
We have \(\frac{S_3}{S_6} = \frac{125}{152}\). Let the sum formula be \(S_n=a(r^n-1)/(r-1)\). So, \(\frac{a(r^3-1)/(r-1)}{a(r^6-1)/(r-1)} = \frac{r^3-1}{r^6-1} = \frac{r^3-1}{(r^3-1)(r^3+1)} = \frac{1}{r^3+1}\). We have \(\frac{1}{r^3+1} = \frac{125}{152} \Rightarrow r^3+1 = \frac{152}{125} \Rightarrow r^3 = \frac{152}{125} - 1 = \frac{27}{125}\). So \(r = 3/5\).
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