The first term of a geometric progression in which all the terms are positive is 50 . The third term is 32 . Find the sum to infinity of the progression.
The first three 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 \(\tan x = \frac { 4 } { 3 }\).
Find the sum of the first twenty terms of the progression.