Mathematics

Problem

Exactly

n

numbers

(n\ge 1)

are inserted between two distinct positive numbers

a

and

b

(a<b)

so that the whole sequence is a geometric progression. a. (i) Derive an expression for the product of the

n

inserted numbers in terms of

a

b

, and

n

. b. (ii) Using the result obtained in part (i), evaluate the product of the five numbers that must be inserted between

4

and

324

to form a geometric progression.