Answer
Pattern: The previous term is being multiplied by 10
The next two terms: 20,000 and 200,000
Work Step by Step
The sequence: 2, 20, 200, 2000, ...
Finding the pattern:
Difference between 1st and 2nd term:
2nd term-1st term=Difference
20-2= 18
Difference between 2nd and 3rd term:
3rd term-2nd term=Difference
200-20=180
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
=$\frac{20}{2}$
=10
Ratio of Second and third term
$\frac{third term}{Second term}$=Ratio
=$\frac{200}{20}$
=10
Ratio of Third and Fourth term
$\frac{Fourth term}{third term}$=Ratio
=$\frac{2000}{200}$
=10
Therefore, the previous term is being multiplied by 10
Finding the next two terms:
Fifth term= Fourth term $ \times$ 10
= 2000 $ \times$ 10
= 20,000
Sixth term= Fifth term $ \times$ 10
= 20,000 $ \times$ 10
= 200,000
Therefore the next two terms are 20,000 and 200,000
