# **SEQUENCES REVIEW - Take Notes!**

### **Part 1: Arithmetic Sequences (5 min)**

**Definition:** A sequence where you ADD the same number each time.
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**Key Terms:**
- **Common difference (d)**: The number you add each time
- **Explicit formula**:$a(n) = a_0+ d(n - 1)$
- a(n) = the nth term
- $a_0$ = INITIAL term / INITIAL Value
- n = term number

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**Example:** 3, 7, 11, 15, ...
- d = 4 (difference between consecutive terms)
- $a_0 = 3$
- Formula: $a(n) = 3 + 4(n - 1)$ or simplified: $a(n) = 4n - 1$

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### **Part 2: Geometric Sequences (5 min)**

**Definition:** A sequence where you MULTIPLY by the same number each time.

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**Key Terms:**
- **Common ratio (r)**: The number you multiply by each time
- **Explicit formula**: $a(n) = a_0 · r^{(n-1)}$

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**Example:** 2, 6, 18, 54, ...
- r = 3 (divide any term by the previous term)
- $a_0 = 2$
- Formula: $a(n) = 2 · 3^{(n-1)}$

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### **Part 3: Practice Problems (10 min)**

**Solve these. Show your work in your notebook! Place your answers in this [link](https://docs.google.com/forms/d/e/1FAIpQLSf_LrgtjAB2NOwIvBg6vjKL9Dxy5iknaPft3D1p713S8b5xSA/viewform?usp=publish-editor).**

**LEVEL 1 (Recall/Define):**
1. What is the common difference in the sequence 5, 9, 13, 17, ...? Write the explicit formula and find the 20th term.

**LEVEL 2 (Apply/Analyze):**
2. The sequence is 80, 40, 20, 10, ...
- Identify the common ratio
- Write the explicit formula
- Calculate the 7th term
- Explain what's happening to the values in this sequence

**LEVEL 3 (Compare/Contrast):**
3. A sequence has a(1) = 6 and a(5) = 486
- Is this arithmetic or geometric? Justify your answer
- Compare how you would find the missing terms using each method
- Write the explicit formula

**HOMEWORK (Create/Evaluate):**
4. **Design Your Own**: Create TWO real-world scenario that could be modeled by an arithmetic sequence and a geometric sequence. Write the first 4 terms, identify the common difference or ratio, and write the explicit formula. Defend why your scenario fits the sequence type you chose. Click the **[link](https://docs.google.com/forms/d/e/1FAIpQLSdR4_usDnnSj-oT5W8ZE_0eN_MMDUZNo6tkJdXuFEZe5BYM6A/viewform?usp=publish-editor)** to submit your work.

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