A) \[\frac{1}{5}\]
B) \[\frac{2}{5}\]
C) \[\frac{3}{5}\]
D) \[\frac{4}{5}\]
Correct Answer: C
Solution :
According to the question, \[\frac{{{S}_{3}}}{{{S}_{6}}}=\frac{a(1-{{r}^{3}})}{1-r}.\frac{1-r}{a(1-{{r}^{6}})}=\frac{125}{152}\] \[\Rightarrow \] \[\frac{1-{{r}^{3}}}{(1-{{r}^{3}})(1+{{r}^{3}})}=\frac{125}{152}\] \[\Rightarrow \] \[\frac{1-{{r}^{3}}}{1+{{r}^{3}}}=\frac{125}{152}\] \[\Rightarrow \] \[1-{{r}^{3}}=\frac{152}{125}\] \[\Rightarrow \] \[{{r}^{3}}=\frac{152}{125}-1=\frac{27}{125}\] \[\Rightarrow \] \[r=\frac{3}{5}\]
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