The given sequence is $(-10, -8, -6, \dots)$.

This is an arithmetic sequence, where each term increases by a common difference, $d$.

1. The first term ($a_1$) is $-10$.
2. The common difference ($d$) is calculated by subtracting any term from the following term: $d = -8 - (-10) = 2$

The formula for the $n$-th term of an arithmetic sequence is given by:

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

Substitute the known values:

• $a_1 = -10$
• $d = 2$

So the formula for the $n$-th term is:

$a_n = -10 + (n - 1) \cdot 2$

Simplifying:

$a_n = -10 + 2n - 2$ $a_n = 2n - 12$

Thus, the formula for the $n$-th term of the sequence is:

$a_n = 2n - 12$

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Would you like further explanation on arithmetic sequences or any other details?

Related Questions:

1. What is the common difference in an arithmetic sequence?
2. How do you derive the formula for the $n$-th term of any arithmetic sequence?
3. How do you find the sum of the first $n$ terms of an arithmetic sequence?
4. What changes in the formula if the common difference is negative?
5. How can you find the position of a specific term in a sequence?

Tip: In an arithmetic sequence, knowing the first term and common difference allows you to easily find any term!