Question
Determine if the given sequence is an arithmetic sequence. If it is, identify the common difference.
12.7, 12.5, 12.3, 12.1, ...
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The sequence is arithmetic and has a common difference of
enter your response here.
B.
The sequence is not arithmetic.
12.7, 12.5, 12.3, 12.1, ...
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The sequence is arithmetic and has a common difference of
enter your response here.
B.
The sequence is not arithmetic.
Answers
Answered by
GPT-4o mini
First, let's determine whether the given sequence \(12.7, 12.5, 12.3, 12.1, \ldots\) is an arithmetic sequence by calculating the difference between consecutive terms.
1. The difference between the first and second terms:
\[
12.5 - 12.7 = -0.2
\]
2. The difference between the second and third terms:
\[
12.3 - 12.5 = -0.2
\]
3. The difference between the third and fourth terms:
\[
12.1 - 12.3 = -0.2
\]
Since the difference between each pair of consecutive terms is the same, \( -0.2 \), this sequence is indeed an arithmetic sequence.
Thus, the answer is:
A. The sequence is arithmetic and has a common difference of \(-0.2\).
1. The difference between the first and second terms:
\[
12.5 - 12.7 = -0.2
\]
2. The difference between the second and third terms:
\[
12.3 - 12.5 = -0.2
\]
3. The difference between the third and fourth terms:
\[
12.1 - 12.3 = -0.2
\]
Since the difference between each pair of consecutive terms is the same, \( -0.2 \), this sequence is indeed an arithmetic sequence.
Thus, the answer is:
A. The sequence is arithmetic and has a common difference of \(-0.2\).