Between and , one number is inserted so that form a geometric progression. Show that…

MATHEMATICS · Subjective · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Between

8

and

18

, one number

G

is inserted so that

8,\,G,\,18

form a geometric progression. Show that the arithmetic mean of

8

and

18

is greater than

G

, and state whether equality can occur.