A) 4
B) \[\,-\,3\]
C) \[-\,2\]
D) 2
Correct Answer: D
Solution :
Let r be the common ratio of the G.P. then \[a+b+c\,=\,xb\] |
\[\Rightarrow \] \[a\,(1+r+{{r}^{2}})\,=\,x(ar)\] |
\[\Rightarrow \] \[x\,=\,\left( 1+r+\frac{1}{r} \right)\] |
where \[\left( r+\frac{1}{r} \right)\,\le \,-\,2\,\text{or}\,\ge \,2\] |
\[\Rightarrow \] Range of x is \[(-\alpha ,-\,1]\,\cup \,[3,\alpha )\,\] |
\[\therefore \]x can not be equal to 2. |
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