1. Lesson 11.4 Alg-1 Write the recursive formula for each sequence
1, 11, 21, 31, …
𝑎 𝑛 =−4+ 𝑛−1 6
4 1 2 , 2, − 1 2 , −3, …
𝑎 𝑛 =3+ 𝑛−1 (−1)
4 Alg-1
5 Alg-1
Calculate the indicated term
Calculate the indicated term
𝑎 5 =−4
𝑎 21 =23
𝑎 5 =−4
𝑎 𝑛 = 𝑎 𝑛−1 +4
𝑎 𝑛 = 𝑎 𝑛−1 −1.2
𝑎 6 =
𝑎 22 =
𝑎 𝑛 = 𝑎 𝑛−1 +4
𝑎 10 =
Lesson Alg-1

2. Homework Corrections
Lesson 11.3 Worksheet
all

3. Calendar 11.4 Unit 2 Test 2 Review Unit 2 Test 2 12.1a 12.1b 12.1c
Monday
Tuesday
Wednesday
Thursday
Friday
11.4
Unit 2 Test 2 Review
Unit 2
Test 2
12.1a
12.1b
12.1c
12.2a
12.2b
12.3a
12.3b
Quiz,
12.4
13.1
13.2
13.3
No School

4. Homework Lesson 11.4 Worksheet all Class Rules!!!
No getting up without asking
2. No talking until activities
3. Take Notes!
DO ALL EXAMPLES
Raise your hand

5. Recursive Formula for Arithmetic Sequences
Lesson 11.4

6. Objective
Given an arithmetic sequence I can write its recursive formula
I can convert from explicit to recursive formula
I can calculate the next term given a recursive formula

7. Last Few Classes… 5, 10, 15, 20, … 𝑎 𝑛 = 𝑎 1 + 𝑛−1 𝑑 𝑎 3 = 15 𝑓(3)=15
Arithmetic Sequences
5, 10, 15, 20, …
𝑎 𝑛 = 𝑎 1 + 𝑛−1 𝑑
Explicit
𝑎 3 = 15
𝑓(3)=15

8. Something new today…

9. Some background…

10. Here’s the idea…
5, 10, 15, 20, …
𝑎 𝑛−1
𝑎 𝑛
𝑎 2
𝑎 3

11. Today’s Task…
5, 10, 15, 20, …
𝑎 𝑛

12. Recursive Formula
𝑎 𝑛 = 𝑎 𝑛−1 +𝑑
Previous term
Common Difference

14. Today’s Tasks Write the recursive formula for a given sequence
Convert recursive to explicit formula
Given a term of a sequence and the common difference, find the next term(s)

15. Today’s Tasks
Write the recursive formula for a given sequence

16. Example 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑 𝑎 𝑛 = 𝑎 𝑛−1 +5 𝑎 𝑛 = 𝑎 𝑛−1 −7
5, 10, 15, 20, …
-3, -10, -17, -24, …
𝑎 𝑛 = 𝑎 𝑛−1 +𝑑
𝑎 𝑛 = 𝑎 𝑛−1 +𝑑
𝑎 𝑛 = 𝑎 𝑛−1 +5
𝑎 𝑛 = 𝑎 𝑛−1 −7

17. Write the recursive formula for each sequence
1, 11, 21, 31, …
4 1 2 , 2, − 1 2 , −3, …
𝑎 𝑛 = 𝑎 𝑛−1 +𝑑
𝑎 𝑛 = 𝑎 𝑛−1 +𝑑
𝑎 𝑛 = 𝑎 𝑛−1 +10
𝑎 𝑛 = 𝑎 𝑛−1 −2 1 2

18. Review Given an arithmetic sequence I can write its recursive formula
I can convert from explicit to recursive formula
I can calculate the next term given a recursive formula

19. What if you had the explicit formula?
𝑎 𝑛 =−3+ 𝑛−1 2
𝑎 𝑛 = 𝑎 𝑛−1 +𝑑
𝑎 𝑛 = 𝑎 𝑛−1 +2

20. What if you had the explicit formula?
𝑎 𝑛 =1.6+ 𝑛−1 (−75)
𝑎 𝑛 = 𝑎 𝑛−1 +𝑑
𝑎 𝑛 = 𝑎 𝑛−1 −75

21. Write the recursive formula for each sequence
𝑎 𝑛 =−4+ 𝑛−1 6
𝑎 𝑛 =3+ 𝑛−1 (−1)
𝑎 𝑛 = 𝑎 𝑛−1 +𝑑
𝑎 𝑛 = 𝑎 𝑛−1 +𝑑
𝑎 𝑛 = 𝑎 𝑛−1 +6
𝑎 𝑛 = 𝑎 𝑛−1 −1

22. Review Given an arithmetic sequence I can write its recursive formula
I can convert from explicit to recursive formula
I can calculate the next term given a recursive formula

23. Using the recursive formula
𝑎 41 =10
𝑎 𝑛 = 𝑎 𝑛−1 +3
𝑎 42 = 13
𝑎 42 = 𝑎 42−1 +3
𝑎 42 = 𝑎 41 +3
𝑎 42 =10+3

24. Using the recursive formula
𝑎 7 =−4
𝑎 𝑛 = 𝑎 𝑛−1 −2
𝑎 8 = −6
𝑎 8 = 𝑎 8−1 −2
𝑎 8 = 𝑎 7 −2
𝑎 8 =−4−2

25. Calculate the indicated term
𝑎 5 =−4
𝑎 21 =23
𝑎 𝑛 = 𝑎 𝑛−1 +4
𝑎 𝑛 = 𝑎 𝑛−1 −1.2
𝑎 6 =
𝑎 22 =
21.8
𝑎 6 = 𝑎 6−1 +4
𝑎 22 = 𝑎 22−1 −1.2
𝑎 6 = 𝑎 5 +4
𝑎 22 = 𝑎 21 −1.2
𝑎 6 =−4+4
𝑎 22 =23−1.2

26. Think about this…

27. Using the recursive formula
𝑎 7 =−4
𝑎 8 −6
𝑎 𝑛 = 𝑎 𝑛−1 −2
𝑎 9 −8
𝑎 11 =
𝑎 10 −10
𝑎 8 = 𝑎 8−1 −2
𝑎 11 −12
𝑎 8 = 𝑎 7 −2
𝑎 8 =−4−2

28. Calculate the indicated term
𝑎 5 =−4
𝑎 6 =0
𝑎 𝑛 = 𝑎 𝑛−1 +4
𝑎 7 =4
𝑎 10 =
𝑎 8 =8
𝑎 9 =12
𝑎 6 = 𝑎 6−1 +4
𝑎 10 =16
𝑎 6 = 𝑎 5 +4
𝑎 6 =−4+4

29. Review Given an arithmetic sequence I can write its recursive formula
I can convert from explicit to recursive formula
I can calculate the next term given a recursive formula

30. Lesson 11.4 Worksheet all Homework End of Class Rules!!!
1. Clean Up your Area
Wait in your chairs
3. I dismiss not the bell
4. Push in your chairs
5. Keep it to a low roar