Find a function that describes the arithmetic sequence.

Question

13, 14, 15, 16,...
Use y to identify each term in the sequence and n to identify each term's position.

Answer 1

To describe the arithmetic sequence 13, 14, 15, 16, ..., we first identify the first term and the common difference.

1. The first term (\(a\)) is 13.
2. 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.