3.43: Logarithmic AP sum

The first three terms of an arithmetic progression are $\lg x$, $\lg(x^{5})$, $\lg(x^{9})$, where $x>0$. Show that the sum to $n$ terms can be written as $n(pn-1)\lg x$, where $p$ is an integer.

Hence find the value of $n$ for which the sum to $n$ terms is equal to $\lg(x^{4950})$.

Given also $S_{n}=-14850$, find the exact value of $x$.