A) \[-1\]
B) \[-3\]
C) \[-2\]
D) \[-1/2\]
Correct Answer: C
Solution :
Let the first term and the common ratio of \[GP\] be \[a\] and \[r\] respectively. Since, any term is the AM of the next two terms. \[\therefore \] \[{{a}_{n}}=\frac{{{a}_{n+1}}{{a}_{n+2}}}{2}\] \[\Rightarrow \] \[a{{r}^{n-1}}=\frac{a{{r}^{n}}+a{{r}^{n+1}}}{2}\] \[\Rightarrow \] \[2=r+{{r}^{2}}\] \[\Rightarrow \] \[{{r}^{2}}+r-2=0\] \[\Rightarrow \] \[(r+2)(r-1)=0\] \[\Rightarrow \] \[r=-2\] \[[\because r\ne 1]\]You need to login to perform this action.
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