Five positive numbers in GP have mean $\frac{31}{10}$ and the sum of reciprocals is $\frac{31}{40}$. If variance $=\frac{m}{n}$ (coprime), then $m+n$ is equal to
Step-by-Step Solution
Key Concept: Let terms be $\frac{a}{r^2},\frac{a}{r},a,ar,ar^2$. Sum $=\frac{31}{2}$ gives $a=2$. Sum of reciprocals gives $r+\frac{1}{r}=\frac{5}{2}\Rightarrow r=2$.
Terms $\frac{1}{2},1,2,4,8$. Variance $=\frac{186}{25}$... $m+n=211$.
Correct Answer: 211