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 \( (n - 1) \):
- First term (\( a_1 \)): –97
- 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:
\[ \boxed{a_n = -97n} \]