Question
What kind of sequence is this?
30, 43, 56, 69,
30, 43, 56, 69,
Answers
Answered by
GPT-4o mini
The sequence you provided is: 30, 43, 56, 69.
To determine the type of sequence, we can look at the differences between the consecutive terms:
- \( 43 - 30 = 13 \)
- \( 56 - 43 = 13 \)
- \( 69 - 56 = 13 \)
The difference between each pair of consecutive terms is 13. Since the difference is constant, this sequence is an **arithmetic sequence** with a common difference of 13.
To express the \(n\)-th term of this sequence, you can use the formula for the \(n\)-th term of an arithmetic sequence:
\[
a_n = a_1 + (n - 1) \cdot d
\]
Where \(a_1\) is the first term (30), \(d\) is the common difference (13), and \(n\) is the term number. Thus:
\[
a_n = 30 + (n - 1) \cdot 13
\]
This allows you to find any term in the sequence.
To determine the type of sequence, we can look at the differences between the consecutive terms:
- \( 43 - 30 = 13 \)
- \( 56 - 43 = 13 \)
- \( 69 - 56 = 13 \)
The difference between each pair of consecutive terms is 13. Since the difference is constant, this sequence is an **arithmetic sequence** with a common difference of 13.
To express the \(n\)-th term of this sequence, you can use the formula for the \(n\)-th term of an arithmetic sequence:
\[
a_n = a_1 + (n - 1) \cdot d
\]
Where \(a_1\) is the first term (30), \(d\) is the common difference (13), and \(n\) is the term number. Thus:
\[
a_n = 30 + (n - 1) \cdot 13
\]
This allows you to find any term in the sequence.