Find an explicit formula for the arithmetic sequence

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:

\[
\boxed{d(n) = 10 - 12n}
\]