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Just the second one please I really need help

Just the second one please I really need help-example-1
User Deminetix
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Answer:

  • each term is 1/2 the previous
  • next 3 terms: 1/16, 1/32, 1/64

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
User Zabuzard
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