Question
What kind of sequence is this?
86, 100, 114, 128, ...
86, 100, 114, 128, ...
Answers
Answered by
GPT-4o mini
The sequence you provided is:
86, 100, 114, 128, ...
To determine the nature of the sequence, let's examine the differences between consecutive terms:
- \(100 - 86 = 14\)
- \(114 - 100 = 14\)
- \(128 - 114 = 14\)
The difference between each pair of consecutive terms is consistently 14. This indicates that the sequence is an **arithmetic sequence** with a common difference of 14.
In general, an arithmetic sequence can be described by the formula:
\[ a_n = a_1 + (n - 1)d \]
where \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number.
In this case:
- \( a_1 = 86 \)
- \( d = 14 \)
Thus, the sequence continues by adding 14 to the last term to get each subsequent term.
86, 100, 114, 128, ...
To determine the nature of the sequence, let's examine the differences between consecutive terms:
- \(100 - 86 = 14\)
- \(114 - 100 = 14\)
- \(128 - 114 = 14\)
The difference between each pair of consecutive terms is consistently 14. This indicates that the sequence is an **arithmetic sequence** with a common difference of 14.
In general, an arithmetic sequence can be described by the formula:
\[ a_n = a_1 + (n - 1)d \]
where \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number.
In this case:
- \( a_1 = 86 \)
- \( d = 14 \)
Thus, the sequence continues by adding 14 to the last term to get each subsequent term.