Find an explicit formula for the arithmetic sequence $$ 170,85,0,85, \ldots $$ Note: the first term should be $$ d(1) $$. $$ d(n)=\square $$

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To find an explicit formula for the arithmetic sequence $$ 170, 85, 0, -85, \ldots $$, we first identify the first term and the common difference.

1. **First term**: The first term $$ d(1) $$ is $$ 170 $$.
2. **Common difference**: To find the common difference $$ d $$, we subtract the first term from the second term:
   $$
   d = 85 - 170 = -85
   $$

Now that we have the first term and the common difference, we can use the formula for the $$ n $$-th term of an arithmetic sequence, which is given by:
$$
d(n) = d(1) + (n - 1) \cdot d
$$

Substituting the values we found:
- $$ d(1) = 170 $$
- $$ d = -85 $$

The formula becomes:
$$
d(n) = 170 + (n - 1)(-85)
$$

Now, we can simplify this expression:
$$
d(n) = 170 - 85(n - 1)
$$
$$
d(n) = 170 - 85n + 85
$$
$$
d(n) = 255 - 85n
$$

Thus, the explicit formula for the arithmetic sequence is:
$$
d(n) = 255 - 85n
$$
The explicit formula for the sequence is $$ d(n) = 255 - 85n $$.

Find an explicit formula for the arithmetic sequence \( 170,85,0,85, \ldots \) Note: the first term should be \( d(1) \). \( d(n)=\square \)

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