A) 1 : 1
B) Common ratio: 1
C) \[{{\left( \text{first term} \right)}^{\text{2}}}\text{: }{{\left( \text{common ratio} \right)}^{\text{2}}}\]
D) \[{{\left( common\text{ }ratio \right)}^{n}}:1\]
Correct Answer: A
Solution :
[a] If the three terms of the GP. be \[\frac{a}{r},\] a and or then \[S=\frac{a}{r}+a+ar=\frac{a}{r}(1+r+{{r}^{2}})\] \[P={{a}^{3}}\] and \[R=\frac{r}{a}+\frac{1}{a}+\frac{1}{ar}=\frac{1}{ar}({{r}^{2}}+r+1)\] Now, \[\frac{{{P}^{2}}{{R}^{3}}}{{{S}^{3}}}=\frac{{{a}^{6}}\frac{1}{{{a}^{3}}{{r}^{3}}}{{({{r}^{2}}+r+1)}^{3}}}{\frac{{{a}^{3}}}{{{r}^{3}}}{{({{r}^{2}}+r+1)}^{3}}}\] So, the required ratio is \[1:1\].
You need to login to perform this action.
You will be redirected in
3 sec
