1.19: Past-paper question 8

The sum of the first 2 terms of a geometric series $\displaystyle G$ is 360
The sum of the 2nd and 3rd terms of $\displaystyle G$ is 288

The $\displaystyle n$th term of $\displaystyle G$ is $\displaystyle U_n$

(a) Show that $\displaystyle U_n = A \left( \frac{4}{5} \right)^{n-1}$ where $\displaystyle A$ is an integer to be found.

(b) Explain why $\displaystyle G$ is convergent.

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

(d) Find the least number of terms for which the sum is greater than 978