Question

Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.

15, 16, 17, 18, ...


an =

Answer 1

The given sequence is an arithmetic sequence where each term increases by 1.

To describe the sequence using \( n \), we can see that:

- The first term (when \( n = 1 \)) is 15.
- The second term (when \( n = 2 \)) is 16.
- The third term (when \( n = 3 \)) is 17.
- The fourth term (when \( n = 4 \)) is 18.

The general form of an arithmetic sequence is given by:

\[
a_n = a_1 + (n - 1)d
\]

Where \( a_1 \) is the first term and \( d \) is the common difference. Here, \( a_1 = 15 \) and \( d = 1 \).

So, the expression for the \( n \)-th term of the sequence is:

\[
a_n = 15 + (n - 1) \cdot 1
\]

This simplifies to:

\[
a_n = 15 + n - 1
\]

\[
a_n = n + 14
\]

Therefore, the expression to describe the sequence is:

\[
a_n = n + 14
\]