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.

Question

–7, –14, –21, –28, ...

an =

Answer 1

The sequence provided is an arithmetic sequence where each term decreases by 7.

To express the \(n\)-th term of the sequence:

1. Identify the first term (\(a_1\)), which is \(-7\).
2. Note the common difference (\(d\)), which is \(-7\) (because \(-14 - (-7) = -7\)).
3. Use the formula for the \(n\)-th term of an arithmetic sequence:

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

Substituting the values:

\[ a_n = -7 + (n - 1)(-7) \]

Simplifying this expression:

\[ a_n = -7 - 7(n - 1) \] \[ a_n = -7 - 7n + 7 \] \[ a_n = -7n \]

Thus, the expression to describe the sequence is:

\[ a_n = -7n \]