Between $1\:\:and\:\:31$ $m$ numbers are inserted so that the resulting sequence is an $A.P.$ and the ratio of $7^{th}\:\;and\:\:(m-1)^{th}$ numbers is $5:9$. find the value of $m$.

Question

$\begin{array}{1 1}13 \\ 12 \\ 14 \\ 15 \end{array}$