The decimal logarithms (base ) of three positive numbers ,

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

Problem

The decimal logarithms (base

10

) of three positive numbers

x

y

, and

z

are in arithmetic progression. If

y=15

and

x+z=45

, find the common ratio

r>1

of the geometric progression formed by

x

y

, and

z

. (a)

\sqrt3

(b)

\dfrac{3+\sqrt5}{2}

(c)

3

(d)

\dfrac{1+\sqrt5}{2}