Question

Find a function that describes the arithmetic sequence.
11.5, 12.5, 13.5, 14.5,...
Use y to identify each term in the sequence and n to identify each term's position.

Answer 1

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 \(11.5, 12.5, 13.5, 14.5, \ldots\):

1. The first term \(a = 11.5\).
2. 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:

\[
y_n = n + 10.5
\]