https://file.aiquickdraw.com/mathbot/file/1728212656497k2896r6v.jpg

Let's go through the worksheet step-by-step.

### Part A: Identifying the Next Term in the Sequence
For each sequence provided, we need to find the next term using the given options:

1. **Sequence**: \( 3, 7, 11, 15, \ldots \)
   - This sequence increases by 4 each time. So, the next term is \( 15 + 4 = 19 \).

2. **Sequence**: \( 3, 6, 12, 24, \ldots \)
   - This sequence doubles each time. So, the next term is \( 24 \times 2 = 48 \).

3. **Sequence**: \( 7, 4, 1, -2, \ldots \)
   - This sequence decreases by 3 each time. So, the next term is \( -2 - 3 = -5 \).

4. **Sequence**: \( -1, 4, -9, 16, \ldots \)
   - The sequence alternates between positive and negative perfect squares. The next term is \( -25 \).

**Answers for Part A**:
1. \( 19 \)
2. \( 48 \)
3. \( -5 \)
4. \( -25 \)

### Part B: Completing the Equations/Formulas
1. **Sequence**: \( 3, 5, 7, \ldots \)
   - The formula given is \( a_n = 2n + 1 \).

2. **Sequence**: \( 5, 10, 15, 20, \ldots \)
   - The formula is \( a_n = 5n \).

3. **Sequence**: \( 2, 7, 12, \ldots \)
   - The formula follows \( a_n = 5n - 3 \).

4. **Sequence**: \( 5, 8, 13, 20, \ldots \)
   - The formula is \( a_n = n^2 + 4 \).

Would you like more details or have any specific questions about these sequences?

### Related Questions
1. What is the general formula for an arithmetic sequence?
2. How do you determine if a sequence is arithmetic or geometric?
3. How can you derive a formula for a quadratic sequence?
4. What is the formula for the \( n \)-th term of a geometric sequence?
5. How do you identify alternating sequences?

### Tip
When finding the next term in a sequence, observe if the sequence is arithmetic, geometric, or follows a specific pattern like alternating signs or powers.

Identify the next term in the sequence and complete the equation/formula for generating the sequence.

This worksheet helps students identify the next term in arithmetic, geometric, and alternating sequences and complete the corresponding formula. Learn key concepts and formulas like a_n = a_1 + (n-1)d for arithmetic sequences and a_n = a_1 * r^(n-1) for geometric sequences. Suitable for Grades 6-8.

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