📚 Topic Summary
Identifying patterns in sequences is a fundamental skill in Algebra 2. A sequence is an ordered list of numbers or other mathematical objects. The goal is to determine the rule or formula that generates the sequence. This can involve arithmetic sequences (where the difference between consecutive terms is constant), geometric sequences (where the ratio between consecutive terms is constant), or more complex patterns that require analyzing differences, ratios, or other relationships between terms. Recognizing these patterns allows you to predict future terms in the sequence and express the sequence using a general formula.
🧩 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Arithmetic Sequence |
A. A sequence where each term is multiplied by a constant ratio to get the next term. |
| 2. Geometric Sequence |
B. The constant value multiplied in a geometric sequence. |
| 3. Common Difference |
C. A sequence where each term is obtained by adding a constant value to the previous term. |
| 4. Common Ratio |
D. The constant value added in an arithmetic sequence. |
| 5. Sequence |
E. An ordered list of numbers or other mathematical objects. |
Match the following:
- 🔢 1 - D
- ➕ 2 - A
- ➗ 3 - E
- ➖ 4 - B
- 🧮 5 - C
✍️ Part B: Fill in the Blanks
A(n) __________ sequence has a constant difference between consecutive terms. To find the next term in a geometric sequence, you __________ the previous term by the common __________. Identifying patterns involves looking for common __________ or __________. Expressing a sequence with a general formula allows us to find any term in the sequence without listing all the preceding terms.
Possible Answers:
- 📈 Arithmetic
- ✖️ Multiply
- ➗ Ratio
- ➕ Differences
- 🧮 Ratios
🤔 Part C: Critical Thinking
Describe a real-world situation where identifying patterns in sequences can be useful. Give a specific example and explain how the pattern recognition helps in that situation.
