Classify the following list of numbers as an arithmetic sequence, a geometric sequence, some other sequence, or not a sequence.

Question

9, 4, −1 , −6 , . . .

(1 point)
Responses

not a sequence
not a sequence

arithmetic sequence
arithmetic sequence

geometric sequence
geometric sequence

some other sequence

Answer 1

To determine the type of sequence represented by the numbers 9, 4, -1, -6, we need to analyze the differences and ratios between consecutive terms.

1. Arithmetic Sequence: An arithmetic sequence has a constant difference between consecutive terms.
   • Difference between 9 and 4: 4 - 9 = -5
   • Difference between 4 and -1: -1 - 4 = -5
   • Difference between -1 and -6: -6 - (-1) = -5

Since the difference is constant at -5, this indicates that the sequence is an arithmetic sequence.

2. Geometric Sequence: A geometric sequence has a constant ratio between consecutive terms.
   • Ratio between 9 and 4: 4 / 9 (not constant with other terms)
   • Ratio between 4 and -1: -1 / 4 (not constant)
   • Ratio between -1 and -6: -6 / -1 = 6 (not constant)

Since the ratios are not constant, this is not a geometric sequence.

Based on our analysis, the correct classification of the sequence 9, 4, -1, -6 is:

Arithmetic sequence.