Mathematics

Problem

Let

a

and

b

be positive real numbers. Suppose

k

geometric means are inserted between

a

and

b

, giving a geometric progression of

k+2

terms. a. (i) Derive, in terms of

a

b

and

k

, an expression for the product of the

k

inserted geometric means. b. (ii) Using the result of part (i), find the product of the five geometric means inserted between 3 and 96.