To describe the arithmetic sequence 13, 14, 15, 16, ..., we first identify the first term and the common difference.
- The first term (\(a\)) is 13.
- The common difference (\(d\)) is 1 (since each term increases by 1).
The general formula for the \(n\)-th term of an arithmetic sequence can be expressed as:
\[ y_n = a + (n - 1)d \]
Substituting the values for \(a\) and \(d\):
\[ y_n = 13 + (n - 1) \cdot 1 \]
This simplifies to:
\[ y_n = 13 + n - 1 \] \[ y_n = n + 12 \]
Thus, the function that describes the arithmetic sequence is:
\[ y = n + 12 \]
Here, \(y\) represents each term in the sequence, and \(n\) represents the position of each term.