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.

–8, –7, –6, –5, ...


an =

Answer 1

To find an expression for the sequence \(-8, -7, -6, -5, \ldots\), we need to identify the pattern in the terms.

The sequence is an arithmetic sequence with:
- The first term \(a_1 = -8\)
- The common difference \(d = -7 - (-8) = 1\)

The \(n\)-th term of an arithmetic sequence can be expressed using the formula:

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

Substituting the values:

\[
a_n = -8 + (n - 1) \cdot 1
\]

Simplifying this:

\[
a_n = -8 + n - 1
\]
\[
a_n = n - 9
\]

Thus, the expression to describe the sequence is:

\[
\boxed{a_n = n - 9}
\]