A) 324
B) 343
C) 243
D) 729
Correct Answer: C
Solution :
Given \[\frac{ar({{r}^{10}}-1)}{r-1}\,=18\] Also \[\frac{\frac{1}{ar}\,\left( 1-\frac{1}{{{r}^{10}}} \right)}{1-\frac{1}{r}}\,=6\Rightarrow \,\,\frac{1}{a{{r}^{11}}}.\,\,\frac{({{r}^{10}}-1)r}{r-1}\,=6\] \[\frac{1}{{{a}^{2}}{{r}^{11}}}.\,\frac{ar({{r}^{10}}-1)}{r-1}\,=6\] ?(2) Form (1) and (2) \[\frac{1}{{{a}^{2}}{{r}^{11}}}.18=6\Rightarrow \,{{a}^{2}}{{r}^{11}}=3\] Now \[P={{a}^{10}}\,{{r}^{55}}\,=({{a}^{2}}{{r}^{11}})\,={{3}^{5}}\,=243\]You need to login to perform this action.
You will be redirected in
3 sec