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=5r3Hence r3=1355=27, so r=3√27=3
Then a=5r=15 and b=ar=15⋅3=45
