1. Sequences F.LE.1, 2, 5 F.BF.1, 2 A.SSE.1.a F.IF.1, 2, 3, 4

2. Arithmetic Sequences: Writing Formulas
Let’s examine Problem 1 on page 236:

3. Arithmetic Sequences: Writing Formulas
Now let’s complete the table:

4. Arithmetic Sequences: Writing Formulas
Now answer the questions on page 237:
Explain how you can calculate the tenth term based on the ninth term.
Determine the 20th term. Explain your calculation.
Is there a way to calculate the 20th term without first calculating the 19th term? If so, describe the strategy.
Describe a strategy to calculate the 93rd term.

5. Arithmetic Sequences: Explicit Formula
General Rule
Example
A lowercase letter is used to name a sequence. 𝑎
The first term, or initial term, is referred to as 𝑎 1 .
𝑎 1 =125
𝑎 2 =143
𝑎 3 =161
The remaining terms are named according to the term number.
A general term of the sequence is referred to as 𝑎 𝑛 , also known as the nth term, where n represents the index.
𝑎 𝑛
The term previous to 𝑎 𝑛 is referred to as 𝑎 𝑛−1 .
𝑎 𝑛−1
The common difference is represented as 𝑑.
𝑑=18
The INDEX is the position of the term (its term number) in a sequence.

6. Arithmetic Sequences: Explicit Formula
The explicit formula for determining the nth term of an arithmetic sequence is:
𝑎 𝑛 = 𝑎 1 +𝑑 𝑛−1
nth term
common difference
1st term
previous term number

7. Arithmetic Sequences: Explicit Formula
Let’s use an explicit formula to determine the 93rd term in the following situation:
𝑎 1 =125 and 𝑑=18
𝑎 𝑛 = 𝑎 1 +𝑑 𝑛−1
𝑎 93 = −1
𝑎 93 =
𝑎 93 =
𝑎 93 =1781
The 93rd term in the sequence is 1781.
This means that Rico will contribute a total of $1781 if the Centipedes hit 92 home runs.

8. Arithmetic Sequences: Explicit Formula
Complete the problems on page 239:
Use the explicit formula to determine the amount of money Rico will contribute if the Centipedes hit:
35 home runs
48 home runs
86 home runs
214 home runs

9. Arithmetic Sequences: Explicit Formula
What if Rico decides to increase his initial contribution to $500 and the amount donated per home run hit to $75.00.
What would change?
𝑎 1 =500 and 𝑑=75

10. Arithmetic Sequences: Explicit Formula
Complete the problems on page 240:
Use the explicit formula to determine the amount of money Rico will contribute if the Centipedes hit:
11 home runs
26 home runs
39 home runs
50 home runs
What are the first 10 terms of the sequence?

11. Geometric Sequences: Writing Formulas
Now let’s read the problem on the bottom of page 240.
How do you know the sequence
1, 2, 4, 8, 16, …
is geometric?
What is the common ratio?
Now complete the table on page 241:

12. Geometric Sequences: Writing Formulas
Now answer the questions on page 241:
Explain how you can calculate the tenth term based on the ninth term.
Determine the 20th term. Explain your calculation.
Is there a way to calculate the 20th term without first calculating the 19th term? If so, describe the strategy.

13. Geometric Sequences: Explicit Formula
General Rule
Example
A lowercase letter is used to name a sequence. 𝑔
The first term, or initial term, is referred to as 𝑔 1 .
𝑔 1 =1
𝑔 2 =2
𝑔 3 =4
The remaining terms are named according to the term number.
A general term of the sequence is referred to as 𝑔 𝑛 , also known as the nth term, where n represents the index.
𝑔 𝑛
The term previous to 𝑔 𝑛 is referred to as 𝑔 𝑛−1 .
𝑔 𝑛−1
The common ratio is represented as 𝑟.
𝑟=2

14. Geometric Sequences: Explicit Formula
The explicit formula for determining the nth term of a geometric sequence is:
𝑔 𝑛 = 𝑔 1 ∙ 𝑟 𝑛−1
nth term
previous term number
1st term
common ratio

15. Geometric Sequences: Explicit Formula
Let’s use an explicit formula to determine the 20th term in the following situation:
𝑔 1 =1 and 𝑟=2
𝑔 𝑛 = 𝑔 1 ∙ 𝑟 𝑛−1
𝑔 20 =1∙ 2 20−1
𝑔 20 =1∙ 2 19
𝑔 20 =1∙524,288
𝑔 20 =524,288
The 20th term in the sequence is 524,288.
This means that after 19 cell divisions, there are a total of 524,288 cells.

16. Geometric Sequences: Explicit Formula
Complete the problems on page 243:
Use the explicit formula to determine the total number of cells after:
11 divisions
14 divisions
18 divisions
22 divisions

17. Geometric Sequences: Explicit Formula
What if we start with 5 different cells whose growth pattern changed such that the mother cell divided into 3 daughter cells?
What would change?
𝑔 1 =5 and 𝑟=3

18. Geometric Sequences: Explicit Formula
Complete the problems on page 244:
Use the explicit formula to the total number of cells after:
4 divisions
7 divisions
13 divisions
16 divisions
What are the first 10 terms of the sequence?

19. Sequences: Recursive Formulas
A RECURSIVE FORMULA expresses each new term of a sequence based on the preceding term in the sequence.
The recursive formula for determining the nth term of an arithmetic sequence is:
𝑎 𝑛 = 𝑎 𝑛−1 +𝑑
nth term
previous term
common difference

20. Sequences: Recursive Formulas
Consider the following sequence:
−2, −9, −16, −23, …
Use the recursive formula to determine the 5th term
𝑎 𝑛 = 𝑎 𝑛−1 +𝑑
𝑎 5 = 𝑎 5−1 +(−7)
𝑎 5 = 𝑎 4 −7
𝑎 5 =−23−7
𝑎 5 =−30
The 5th term in the sequence is −30.

21. Sequences: Recursive Formulas
The recursive formula for determining the nth term of a geometric sequence is:
𝑔 𝑛 = 𝑔 𝑛−1 ∙𝑟
nth term
previous term
common ratio

22. Sequences: Recursive Formulas
Consider the following sequence:
4, 12, 36, 108, …
Use the recursive formula to determine the 5th term
𝑔 𝑛 = 𝑔 𝑛−1 ∙𝑟
𝑔 5 = 𝑔 5−1 ∙ (3)
𝑔 5 = 𝑔 4 ∙ (3)
𝑔 5 =108∙ (3)
𝑔 5 =324
The 5th term in the sequence is 324.

23. Using Recursive Formulas
Complete Problems 1 & 2 on pages 246 & 247 for homework.