An arithmetic sequence can be expressed in the form:
\[ d(n) = a + (n - 1) \cdot r \]
where \( a \) is the first term, \( n \) is the term number, and \( r \) is the common difference between the terms.
In the given sequence:
- The first term \( a = -2 \).
- To find the common difference \( r \), we can calculate the difference between any two consecutive terms. For example:
\[ r = -14 - (-2) = -14 + 2 = -12 \]
We can verify this by checking the next pair:
\[ -26 - (-14) = -26 + 14 = -12 \]
\[ -38 - (-26) = -38 + 26 = -12 \]
The common difference \( r = -12 \) is consistent between the terms.
Now, substituting \( a \) and \( r \) into the formula for an arithmetic sequence, we get:
\[ d(n) = -2 + (n - 1) \cdot (-12) \]
This simplifies to:
\[ d(n) = -2 - 12(n - 1) \]
Expanding the expression gives:
\[ d(n) = -2 - 12n + 12 \] \[ d(n) = 10 - 12n \]
Thus, the explicit formula for the arithmetic sequence is:
\[ \boxed{d(n) = 10 - 12n} \]