A) \[-2\]
B) 2
C) 1
D) 1/2
Correct Answer: B
Solution :
Under given conditions, we get \[\Rightarrow \] \[\frac{a({{r}^{6}}-1)}{(r-1)}=9.\frac{a({{r}^{3}}-1)}{(r-1)}\] \[(\because \ r>1)\] \[\Rightarrow \] \[{{r}^{6}}-1=9{{r}^{3}}-9\]\[\Rightarrow \] \[{{({{r}^{3}})}^{2}}-9({{r}^{3}})+8=0\] \[\Rightarrow \] \[({{r}^{3}}-1)({{r}^{3}}-8)=0\] \[\Rightarrow \] \[r=1,\ \omega ,\ {{\omega }^{2}}\] and \[r=2\]. But \[r=1,\ \omega ,\ {{\omega }^{2}}\] cannot satisfy the given condition. Hence\[r=2\].
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