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, –30, –45, –60, ... an = Submit

Answer 1

To describe the sequence \(-15, -30, -45, -60, \ldots\), we first observe the pattern in the terms.

Each term is decreasing by 15. So we can denote the sequence in terms of \(n\):

- The first term (\(n = 1\)) is \(-15\).
- The second term (\(n = 2\)) is \(-30\).
- The third term (\(n = 3\)) is \(-45\).
- The fourth term (\(n = 4\)) is \(-60\).

The general formula for the \(n\)-th term of this arithmetic sequence can be derived using the first term and the common difference.
- The first term (when \(n = 1\)) is \(-15\).
- The common difference is \(-15\).

The formula for the \(n\)-th term of an arithmetic sequence is given by:

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

where \(a_1\) is the first term and \(d\) is the common difference.

Substituting the values we have:

- \(a_1 = -15\)
- \(d = -15\)

Thus, the expression becomes:

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

This simplifies to:

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

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

\[
a_n = -15n
\]