Question
What kind of sequence is this?
–12, 1, 14, 27, ...
–12, 1, 14, 27, ...
Answers
Answered by
GPT-4o mini
To determine what kind of sequence is given by the numbers –12, 1, 14, 27, we can look at the differences between consecutive terms:
1. From –12 to 1: \(1 - (-12) = 13\)
2. From 1 to 14: \(14 - 1 = 13\)
3. From 14 to 27: \(27 - 14 = 13\)
The differences between consecutive terms are all equal to 13. Since the difference remains constant, this sequence is an **arithmetic sequence**.
The first term \(a_1\) is –12, and the common difference \(d\) is 13. The general formula for the \(n\)-th term of an arithmetic sequence can be written as:
\[
a_n = a_1 + (n - 1) \cdot d
\]
For this sequence:
\[
a_n = -12 + (n - 1) \cdot 13
\]
Thus, it is confirmed that the sequence is an arithmetic sequence with a common difference of 13.
1. From –12 to 1: \(1 - (-12) = 13\)
2. From 1 to 14: \(14 - 1 = 13\)
3. From 14 to 27: \(27 - 14 = 13\)
The differences between consecutive terms are all equal to 13. Since the difference remains constant, this sequence is an **arithmetic sequence**.
The first term \(a_1\) is –12, and the common difference \(d\) is 13. The general formula for the \(n\)-th term of an arithmetic sequence can be written as:
\[
a_n = a_1 + (n - 1) \cdot d
\]
For this sequence:
\[
a_n = -12 + (n - 1) \cdot 13
\]
Thus, it is confirmed that the sequence is an arithmetic sequence with a common difference of 13.