Select the formula for nth terms of the sequence (-10,-8,-6)

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!

Learn how to find the nth term of the arithmetic sequence (-10, -8, -6). This solution uses the formula for arithmetic sequences and covers key concepts such as common difference and term calculation. Suitable for students in Grades 6-8.

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