Tell whether the sequence 1/3, 0, 1, -2 is arithmetic, geometric, or neither. find the next three terms of the sequence.

a. neither; 7, -20, 61
b. geometric; 7, -20, 61
c. arithmetic; -1/3, 1 1/3, 3
d. geometric; -3 1/3, -5 5/9, -9 7/27

A. neither; 7, -20, 61

Step-by-step explanation:

The sequence 1/3, 0, 1, -2 ...

The difference between the terms are; -1/3, 1, -3

Looking the difference between consecutive terms in the sequence, we can predict the next differences between the following terms, as the differences form a geometric sequence;

Therefore; -1/3, 1, -3, 9, -27, 81

Thus; the sequence will be;

1/3, 0, 1, -2 , (-2+9), (-2+9+-27), (-2+9+-27+81)

1/3, 0, 1, -2, 7, -20, 61

Hence the next three terms are; 7, -20, 61

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