Question

Tell whether the sequence 1 , 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 , 1 1 , 3 33
D.geometric;−31,−55,−9 7 3 9 27

Answer 1

A. neither; 7, -20, 61

Explanation:

The given terms do not have a common difference, so the sequence is not arithmetic.

The given terms do not have a common ratio, so the sequence is not geometric. (Any sequence with 0 as a term cannot be geometric.)

The sequence is neither arithmetic or geometric.

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The first differences of the terms of this sequence are ...

-1, 1, -3

If we choose answer A (the only selection with "neither"), it suggests the next 3 terms are 7, -20, 61. These terms make the next differences be 9, -27, and 81. After the first term, the differences of the proposed sequence have a common ratio of -3. However, the first term needs to be 1/3 in order for that rule to be consistent for the whole sequence.