The sequence given is: 2, -2, -6, ...

This suggests that the terms follow a linear pattern, where each term decreases by 4. To find an explicit formula for the $n$-th term, $a_n$, of this sequence, let's break it down.

1. The first term $a_1 = 2$.
2. The difference between consecutive terms is constant and equal to $-4$.

This is an arithmetic sequence, and the general formula for the $n$-th term of an arithmetic sequence is:

$a_n = a_1 + (n-1) \cdot d$

Where:

• $a_1 = 2$ (the first term),
• $d = -4$ (the common difference),
• $n$ is the term number.

Substituting the values for $a_1$