Question

Classify each sequence:1/3, 2/3, 4/3, 8/3,...

a. arithmetic
b. geometric
c. neither​

Answer 1

b. Geometric

Explanation:

(1/3)×2 = (2/3)

(2/3)×2 = 4/3

(4/3)×2 = 8/3

2 is the common ratio

Answer 2

b. geometric

Explanation:

The terms don't have a common difference, but they do have a common ratio: 2. A sequence in which terms have a common ratio is a geometric sequence.

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Differences are ...

2/3 -1/3 = 1/3

4/3 -2/3 = 2/3 . . . . not the same

Ratios are ...

(2/3)/(1/3) = 2

(4/3)/(2/3) = 2

(8/3)/(4/3) = 2 . . . . ratios are common between pairs of terms