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We are given the following recursive sequence formula:

\[
a_1 = -2
\]
\[
a_n = a_{n-1} + 8
\]

We need to find \( a_2 \), \( a_3 \), and \( a_4 \).

### Step-by-step calculations:

1. **Finding \( a_2 \):**
   \[
   a_2 = a_1 + 8 = -2 + 8 = 6
   \]

2. **Finding \( a_3 \):**
   \[
   a_3 = a_2 + 8 = 6 + 8 = 14
   \]

3. **Finding \( a_4 \):**
   \[
   a_4 = a_3 + 8 = 14 + 8 = 22
   \]

### Final answers:
\[
a_2 = 6, \quad a_3 = 14, \quad a_4 = 22
\]

Would you like any further explanations or more details?

Here are 5 follow-up questions to deepen your understanding:
1. What type of sequence is represented by the given formula?
2. Can you generalize the formula for \(a_n\) without recursion?
3. How would the sequence change if \(a_1\) were different?
4. Can you express the sequence using a geometric or arithmetic progression?
5. What would \(a_5\) be?

**Tip**: Recognizing patterns in sequences can help you derive general formulas for any term in the sequence.

Find a2, a3, and a4. a1 = -2, an = an-1 + 8. Write your answers as integers or fractions in simplest form.

Learn how to find specific terms in an arithmetic sequence using the recursive formula a_n = a_(n-1) + d, where d is the common difference. In this example, we calculate a2, a3, and a4 from a sequence where a1 = -2 and the common difference is 8. Suitable for students in Grades 6-8.

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