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.

–2, –4, –6, –8, ...


an =

Answer 1

The given sequence is: \(-2, -4, -6, -8, \ldots\)

This sequence is an arithmetic sequence where each term decreases by 2.

To write an expression for the \(n\)-th term of the sequence, we can identify the first term (\(a_1 = -2\)) and the common difference (\(d = -2\)). The formula for the \(n\)-th term of an arithmetic sequence can be expressed as:

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

Substituting the known values into the formula:

\[
a_n = -2 + (n-1)(-2)
\]

Now, simplifying this expression:

\[
a_n = -2 - 2(n-1)
\]
\[
a_n = -2 - 2n + 2
\]
\[
a_n = -2n
\]

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

\[
a_n = -2n
\]