Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
2, comma, 10, comma, 18, comma, point, point, .
2,10,18,...

Let's analyze the sequence: 2, 10, 18, ...

### Step 1: Check if it's Arithmetic
For an arithmetic sequence, the difference between consecutive terms should be constant.

- Difference between the second term and the first term:
  \( 10 - 2 = 8 \)

- Difference between the third term and the second term:
  \( 18 - 10 = 8 \)

Since the difference between consecutive terms is constant (8), this is an **arithmetic sequence**.

### Step 2: Common Difference
The common difference \( d \) is:
\[
d = 8
\]

Thus, the sequence is **arithmetic** with a common difference of \( 8 \).

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:
1. How can you express the \(n\)-th term of an arithmetic sequence?
2. How would the sequence change if the common difference were negative?
3. What is the sum of the first \(n\) terms of an arithmetic sequence?
4. Can an arithmetic sequence ever become geometric? Why or why not?
5. How would you graph the terms of an arithmetic sequence?

**Tip:** In an arithmetic sequence, the \(n\)-th term can be found using the formula \( a_n = a_1 + (n - 1)d \), where \(a_1\) is the first term, and \(d\) is the common difference.

Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 2, 10, 18, ...

Learn how to determine whether a sequence is arithmetic or geometric with the sequence 2, 10, 18. This problem explains the concept of common difference and provides a step-by-step solution for arithmetic sequences. Suitable for students in Grades 6-8.

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