9514 1404 393
Answer:
- each term is 1/2 the previous
- next 3 terms: 1/16, 1/32, 1/64
Step-by-step explanation:
In algebra classes, we generally study two kinds of sequences: arithmetic and geometric.
Arithmetic sequences have a common difference. That is, the difference between any adjacent terms is the same for all terms in the sequence. Here, the differences are 1/4-1/2 = -1/4, 1/8 -1/4 = -1/8. These differences are NOT the same, so this is NOT an arithmetic sequence.
Geometric sequences have a common ratio. That is, the ratio of any term to the previous one is the same for all terms of the sequence. Here, the ratios are (1/4)/(1/2) = 1/2, (1/8)/(1/4) = 1/2. These ratios are the same, so this is a geometric sequence.
In finding this common ratio, we have discovered the rule for new terms:
each term is 1/2 the value of the previous term
Using this rule, we can find the next 3 terms to be ...
- 1/8 × 1/2 = 1/16
- 1/16 × 1/2 = 1/32
- 1/32 × 1/2 = 1/64
