A) 108
B) 27
C) 54
D) 9
Correct Answer: B
Solution :
\[S={{\left( \frac{3}{4} \right)}^{3}}+{{\left( \frac{6}{4} \right)}^{3}}+{{\left( \frac{9}{4} \right)}^{3}}+{{\left( \frac{12}{4} \right)}^{3}}+...\] 15 term |
\[=\frac{27}{64}\sum\limits_{r\,=\,1}^{15}{{{r}^{3}}}\] |
\[=\frac{27}{64}.{{\left[ \frac{15(15+1)}{2} \right]}^{2}}\] |
\[=225\text{ }K\](Given in question) |
\[K=27.\] |
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