An arithmetic sequence can be described using the formula:
\[ y_n = a + (n - 1)d \]
where:
- \(y_n\) is the \(n\)-th term in the sequence,
- \(a\) is the first term,
- \(d\) is the common difference,
- \(n\) is the position of the term in the sequence.
For the given sequence \(11.5, 12.5, 13.5, 14.5, \ldots\):
- The first term \(a = 11.5\).
- The common difference \(d = 12.5 - 11.5 = 1\).
Now we can substitute these values into the formula:
\[ y_n = 11.5 + (n - 1) \cdot 1 \]
Simplifying this, we get:
\[ y_n = 11.5 + n - 1 \] \[ y_n = n + 10.5 \]
Therefore, the function that describes the arithmetic sequence is:
\[ y_n = n + 10.5 \]
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