An arithmetic sequence is defined by its first term and the common difference between consecutive terms.
In the given sequence:
- The first term \( a_1 = 170 \).
- The second term \( a_2 = 85 \).
To find the common difference \( d \), we can calculate:
\[ d = a_2 - a_1 = 85 - 170 = -85 \]
Now that we have the first term \( a_1 = 170 \) and the common difference \( d = -85 \), we can express the \( n \)-th term of the arithmetic sequence using the formula:
\[ a_n = a_1 + (n - 1) d \]
Substituting the values of \( a_1 \) and \( d \):
\[ a_n = 170 + (n - 1)(-85) \]
Simplifying this:
\[ a_n = 170 - 85(n - 1) \] \[ a_n = 170 - 85n + 85 \] \[ a_n = 255 - 85n \]
Thus, the explicit formula for the \( n \)-th term of the arithmetic sequence is:
\[ d(n) = 255 - 85n \]