A) \[2({{5}^{2}})\]
B) \[4({{5}^{2}})\]
C) \[{{5}^{4}}\]
D) \[{{5}^{3}}\]
Correct Answer: C
Solution :
Here, \[{{a}_{1}},{{a}_{2}},\],.......\[{{a}_{10}}\]are in G.P. Let the common ratio be r. Given,\[\frac{{{a}_{3}}}{{{a}_{1}}}=25\Rightarrow \frac{{{a}_{1}}{{r}^{2}}}{{{a}_{1}}}=25\Rightarrow {{r}^{2}}=25\Rightarrow r=\pm 5\] Now,\[\frac{{{a}_{9}}}{{{a}_{5}}}=\frac{{{a}_{1}}{{r}^{8}}}{{{a}_{1}}{{r}^{4}}}={{r}^{4}}={{5}^{4}}\]
You need to login to perform this action.
You will be redirected in
3 sec
