A) \[\frac{2}{5}\]
B) \[\frac{2}{3}\]
C) \[\frac{1}{3}\]
D) \[\frac{1}{4}\]
Correct Answer: C
Solution :
Consider the GP \[a,ar,a{{r}^{2}},a{{r}^{3}}......\] It's first term is a and common ratio is r. \[\therefore \] \[a=2(ar+a{{r}^{2}}+a{{r}^{3}}+...)\] \[\Rightarrow \] \[1=2(r+{{r}^{2}}+{{r}^{3}}+...)\] \[\Rightarrow \] \[1=\frac{2r}{1-r}\] \[\Rightarrow \] \[1-r=2r\] \[\Rightarrow \] \[3r=1\] \[\Rightarrow \] \[r=\frac{1}{3}\]
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