(i)[2]
The first two terms of a geometric progression are $p$ and $2p$ respectively, where $p$ is a positive constant. The sum of the first $n$ terms is greater than $1000p$. Show that $2^n > 1001$.
(ii)[5]
In a different case, $p$ and $2p$ are the first and second terms of an arithmetic progression respectively. The $n$th term is $336$ and the sum of the first $n$ terms is $7224$. Write down two equations in $n$ and $p$ and hence find the values of $n$ and $p$.