Question

Find two geometric means between 5 and 135

Answer 1

Answer:

We are effectively looking for a and b such that 5, a, b, 135 is a geometric sequence.

This sequence has common ratio 3√1355=3, hence a=15 and b=45

Explanation:

In a geometric sequence, each intermediate term is the geometric mean of the term before it and the term after it.

So we want to find a and b such that 5, a, b, 135 is a geometric sequence.

If the common ratio is r then:

a=5rb=ar=5r2135=br=5r3

Hence r3=1355=27, so r=3√27=3

Then a=5r=15 and b=ar=15⋅3=45