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.

–4, –3, –2, –1, ...


an =

Answer 1

To describe the sequence \(-4, -3, -2, -1, \ldots\) using \(n\) to represent the position of a term, we can observe that the sequence increases by \(1\) for each subsequent term.

The first term (when \(n = 1\)) is \(-4\), the second term (when \(n = 2\)) is \(-3\), the third term (when \(n = 3\)) is \(-2\), and the fourth term (when \(n = 4\)) is \(-1\).

We can see a pattern in how the terms relate to \(n\). Each term in the sequence can be expressed as:

\[
a_n = -4 + (n - 1)
\]

This simplifies to:

\[
a_n = -4 + n - 1 = n - 5
\]

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

\[
a_n = n - 5
\]