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