hat is the formula for the nth term of an arithmetic sequence?

The formula for the \( n \)-th term of an arithmetic sequence is:

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

Where:
- \( a_n \) is the \( n \)-th term,
- \( a_1 \) is the first term of the sequence,
- \( d \) is the common difference between consecutive terms,
- \( n \) is the term number.

Would you like more details or examples about this formula?

Here are five related questions:
1. How do you find the common difference \( d \) in an arithmetic sequence?
2. Can you derive the formula for the sum of the first \( n \) terms of an arithmetic sequence?
3. How is an arithmetic sequence different from a geometric sequence?
4. How do you determine whether a given sequence is arithmetic?
5. What happens if the common difference \( d \) is negative?

**Tip:** In an arithmetic sequence, the common difference \( d \) remains constant throughout the sequence.

What is the formula for the nth term of an arithmetic sequence?

Discover how to find the nth term in an arithmetic sequence with this detailed guide. The formula a_n = a_1 + (n - 1) * d is explained, along with key concepts like common difference and first term. Suitable for students in Grades 8-10 learning basic algebra.

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