Let three real numbers be in arithmetic progression and be in geometric progression

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

Problem

Let three real numbers

a, b, c

be in arithmetic progression and

a + 1, b, c + 3

be in geometric progression. If

a > 10

and the arithmetic mean of

a, b

and

c

is 8, then the cube of the geometric mean of

a, b

and

c

is (A) 120 (B) 312 (C) 316 (D) 128