(a)[3]
In a geometric progression where every term is positive, the first term is $50$ and the third term is $32$. Find the sum to infinity of this progression.
(b(i))[3]
The three initial terms of an arithmetic progression are $2\sin x$, $3\cos x$ and $(\sin x + 2\cos x)$ respectively, where $x$ is an acute angle. Show that $\tan x = \frac{4}{3}$.
(b(ii))[3]
Find the total of the first twenty terms of the progression.