Let the positive numbers a_1, a_2, a_3, a_4 and a_5 be in a G.P. Let their mean and variance be 31/10 and m/n respectively, where m and n are…

Let the positive numbers $\displaystyle \mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3, \mathrm{a}_4$ and $\displaystyle \mathrm{a}_5$ be in a G.P. Let their mean and variance be $\displaystyle \frac{31}{10}$ and $\displaystyle \frac{m}{n}$ respectively, where m and n are co-prime. If the mean of their reciprocals is $\displaystyle \frac{31}{40}$ and $\displaystyle a_3+a_4+a_5=14$, then $\displaystyle m+n$ is equal to $\displaystyle \_\_\_\_$.