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• **Turn in your Fall break Packet to the basket.**

• **Find the next/missing numbers in each pattern.**

**1. 1,__,5,7,__,…**

**2. 2,4,6,8,__,__,__,…**

**3. 1,3,9,27,__,…**

**4. 1,-3,9,-27,__,…**

**5. 240,__,60,__,15,…**

**Coordinate Algebra**

**UNIT QUESTION: **How can we use real-world situations to construct and compare linear and exponential models and solve problems?

Standards: MCC9-12.A.REI.10, 11, F.IF.1-7, 9, F.BF.1-3, F.LE.1-3, 5

**Today’s Question: **What is a Sequence? Is a sequence a function? Can you find the nth term and the domain of a sequence?

Standard: MCC9

‐

12.R.IF.3

**A sequence of terms that have a common difference between them**

**A sequence of terms that have a common ratio between them**

**Arithmetic or Geometric?**

*Example 1***:**

**-22, -15, -8, -1, …**

**Arithmetic d = 7**

**Arithmetic or Geometric?**

*Example 2***:**

**256, 64, 16, 4, …**

**Geometric r = 1/4**

**Arithmetic or Geometric?**

*Example 3***:**

**7, 4, 1, -2, -5**

**Arithmetic d = -3**

**Arithmetic or Geometric?**

*Example 4***:**

4

3 9 81

,...

**NEITHER**

**Arithmetic or Geometric?**

*Example 5***:**

**NEITHER **

**Formula used to find the n th term of a sequence**

*a n*

*a*

1

*n*

1

*d*

*a n*

*n*

1

**Find the common difference/ratio, the explicit formula, and the tenth term.**

**3, 9, 15, 21, …**

*a a n n*

*a*

3

1

*n n*

1

*d*

**d = 6 a n**

**= 6n – 3 **

*a*

10

**a**

**10**

**= 57 **

3

**Find the common difference/ratio, the explicit formula, and the seventh term.**

*a*

**3, 1.5, 0.75, 0.375, …**

*n*

*n*

1

*r*

1.5

3

0.5

*a n*

*n*

1

*a*

7

*a*

7

0.0456875

**The fifth term is 1,792. The constant ratio is 4. Write the explicit formula.**

*a*

5

1792 and

*n*

5 and

*r*

4

*a n*

*n*

1

1792

*a*

1

1

*a n*

*n*

1