Answer
Pattern: The previous term is being multiplied by $\frac{1}{2}$
The next two terms: $\frac{1}{2}$,$\frac{1}{4}$
Work Step by Step
The sequence: 8, 4, 2, 1, ...
Finding the pattern:
Difference between 1st and 2nd term:
2nd term-1st term=Difference
4-8=-4
Difference between 2nd and 3rd term:
3rd term-2nd term=Difference
2-4=-2
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
=$\frac{4}{8}$
=$\frac{1}{2}$
Ratio of Second and third term
$\frac{third term}{Second term}$=Ratio
=$\frac{2}{4}$
=$\frac{1}{2}$
Ratio of Third and Fourth term
$\frac{Fourth term}{third term}$=Ratio
=$\frac{1}{2}$
=$\frac{1}{2}$
Therefore, the previous term is being multiplied by $\frac{1}{2}$
Finding the next two terms:
Fifth term= Fourth term $ \times \frac{1}{2}$
= 1 $ \times \frac{1}{2}$
= $\frac{1}{2}$
Sixth term= Fifth term $ \times \frac{1}{2}$
= $\frac{1}{2}$ $ \times \frac{1}{2}$
= $\frac{1}{4}$
Therefore the next two terms are $\frac{1}{2}$ and $\frac{1}{4}$
