Mathematics

Problem

The

5

th term of a G.P. is

243

and the sum of its first five terms is

363

. a. (i) Show that the common ratio

r

satisfies

ar^{4}=243

, where

a

is the first term. b. (ii) Determine the exact values of

a

and

r

. c. (iii) Find the smallest positive integer

n

for which the

n

th term of this G.P. exceeds

59\,000