Question
What kind of sequence is this?
191, 173, 155, 137, ...
A) arithmetic
B) geometric
C) both
D) neither
191, 173, 155, 137, ...
A) arithmetic
B) geometric
C) both
D) neither
Answers
Answered by
GPT-4o mini
To determine the type of sequence, we need to analyze the differences between the terms.
The given sequence is:
191, 173, 155, 137, ...
Now, let's calculate the differences between consecutive terms:
1. \( 191 - 173 = 18 \)
2. \( 173 - 155 = 18 \)
3. \( 155 - 137 = 18 \)
The difference between each consecutive term is constant at \( 18 \). This means the sequence is an arithmetic sequence because in an arithmetic sequence, the difference between consecutive terms is constant.
To check if it is a geometric sequence, we would look for a constant ratio between consecutive terms:
1. \( \frac{173}{191} \approx 0.905 \)
2. \( \frac{155}{173} \approx 0.896 \)
3. \( \frac{137}{155} \approx 0.887 \)
The ratios are not constant, which means that it is not a geometric sequence.
Given this analysis, the answer is:
A) arithmetic
The given sequence is:
191, 173, 155, 137, ...
Now, let's calculate the differences between consecutive terms:
1. \( 191 - 173 = 18 \)
2. \( 173 - 155 = 18 \)
3. \( 155 - 137 = 18 \)
The difference between each consecutive term is constant at \( 18 \). This means the sequence is an arithmetic sequence because in an arithmetic sequence, the difference between consecutive terms is constant.
To check if it is a geometric sequence, we would look for a constant ratio between consecutive terms:
1. \( \frac{173}{191} \approx 0.905 \)
2. \( \frac{155}{173} \approx 0.896 \)
3. \( \frac{137}{155} \approx 0.887 \)
The ratios are not constant, which means that it is not a geometric sequence.
Given this analysis, the answer is:
A) arithmetic