Mathematics

Problem

Suppose

a

b

and

c

are positive real numbers such that

\log_{10} a

\log_{10} b

and

\log_{10} c

are consecutive terms of an arithmetic progression. (i) Prove that

a

b

and

c

are consecutive terms of a geometric progression. (ii) If

a = 25

and

c = 400

, find the value of

b

. (iii) Verify directly that the value of

b

obtained in part (ii) satisfies the relationship proved in part (i).