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.

–97, –194, –291, –388, ...


an =

Answer 1

The given sequence is an arithmetic sequence where each term decreases by 97 from the previous term.

To find the formula for the \( n \)-th term \( a_n \), we can start with the first term and then add the common difference multiplied by \( (n - 1) \):

1. First term (\( a_1 \)): –97
2. Common difference (\( d \)): \( -194 - (-97) = -97 \)

The general formula for an arithmetic sequence is given by:

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

Substituting the known values:

\[
a_n = -97 + (n - 1) \cdot (-97)
\]

This can be simplified:

\[
a_n = -97 - 97(n - 1)
\]
\[
= -97 - 97n + 97
\]
\[
= -97n
\]

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

\[
\boxed{a_n = -97n}
\]