Answer
Pattern: The previous term is being multiplied by 2
The next two terms: 72, 144
Work Step by Step
The sequence: 4.5, 9, 18, 36, ...
Finding the pattern:
Difference between 1st and 2nd term:
2nd term-1st term=Difference
9-4.5=4.5
Difference between 2nd and 3rd term:
3rd term-2nd term=Difference
18-9=9
We see that the difference is not constant thus the sequence is not arithmetic. Thus we need to find the ratio between consecutive terms.
Ratio of first and second term
$\frac{Second term}{first term}$=Ratio
=$\frac{9}{4.5}$
=2
Ratio of Second and third term
$\frac{third term}{Second term}$=Ratio
=$\frac{18}{9}$
=2
Ratio of Third and Fourth term
$\frac{Fourth term}{third term}$=Ratio
=$\frac{36}{18}$
=2
Therefore, the previous term is being multiplied by 2
Finding the next two terms:
Fifth term= Fourth term $ \times $ 2
= 36 $ \times $ 2
= 72
Sixth term= Fifth term $ \times $ 2
= 72 $ \times $ 2
= 144
Therefore the next two terms are 72 and 144
