1.14: Past-paper question 7

A geometric series $\displaystyle G$ with common ratio $\displaystyle r$, has first term 16 and third term $\displaystyle \frac{2704}{625}$

(a) Find the two possible values of $\displaystyle r$

Given that $\displaystyle r > 0$

(b) find the sum to infinity of $\displaystyle G$

The sum to $\displaystyle n$ terms of $\displaystyle G$ is greater than 33

(c) Find, using logarithms, the least possible value of $\displaystyle n$

Show your working clearly.