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

some other sequence
some other sequence

geometric sequence
geometric sequence

arithmetic sequence
arithmetic sequence

not a sequence

Answer 1

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

1. Arithmetic Sequence: In an arithmetic sequence, the difference between consecutive terms is constant.

   • The difference between 9 and 4 is $4-9=-5$.
   • The difference between 4 and -1 is $-1-4=-5$.
   • The difference between -1 and -6 is $-6-(-1)=-5$.

   Since the difference is constant (-5), this qualifies as an arithmetic sequence.

2. Geometric Sequence: In a geometric sequence, the ratio of consecutive terms is constant.

   • The ratio between 9 and 4 is $4/9$.
   • The ratio between 4 and -1 is $-1/4$.
   • The ratio between -1 and -6 is $-6/(-1)=6$.

   The ratios are not constant, so this is not a geometric sequence.

Based on this analysis, the correct classification for the sequence 9, 4, -1, -6 is:

arithmetic sequence.