Let and be distinct positive numbers with

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Let

a

and

b

be distinct positive numbers with

a<b

. A single geometric mean

G

is inserted so that

a,\,G,\,b

are in geometric progression. Which of the following is always true? (a)

G = \dfrac{a + b}{2}

(b)

a < G < b

(c)

G = ab

(d)

G = \dfrac{2ab}{a+b}