3.45: GP fifteenth term and sum near infinity

0606/13/O/N/22 — Question 5 · 7 marks

(a)
A GP has u15=18u12u_{15}=\tfrac18 u_{12} and S=5S_{\infty}=5. Find aa and rr.
[4]
(b)
Find the least nn such that Sn>4.999S_{n}>4.999.
[3]