1. Warm up f(x) = 3x + 5, g(x) = x – 15, k(x) = -9 Find 2f(x) + g(x).
Find g(x) – f(x) – k(x).

2. Arithmetic Sequence
A sequence of terms that have a common difference between them

3. Geometric Sequence
A sequence of terms that have a common ratio between them

4. Explicit Formula
Formula used to find the nth term of a sequence

5. Explicit Formula for Arithmetic Sequence

6. Explicit Formula for Geometric Sequence

7. Arithmetic or Geometric?
Example:
-22, -15, -8, -1, …
Arithmetic
d = 7

8. Arithmetic or Geometric?
Example:
7, 4, 1, -2, -5
Arithmetic
d = -3

9. Arithmetic or Geometric?
Example:
256, 64, 16, 4, …
Geometric
r = 1/4

10. Arithmetic or Geometric?
Example:
Geometric
r = 2/3

11. Find the common difference, the explicit formula, and the tenth term.
3, 9, 15, 21, …
d = 6
an = 6n – 3
a10 = 57

12. Find the common ratio, the explicit formula, and the seventh term.
3, 1.5, 0.75, 0.375, …

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

14. Arithmetic & Geometric Sequences
Recursive

15. Recursive Formula
a formula used to find the next term of a sequence when the previous term is known

16. Recursive Formula for Arithmetic Sequence

17. The first term is 1 for an = an-1 – 2. Find the next term.
iRespond Question
Fill-In F
E0F52DA BFAF-D16246ED6B41
A.) -1;;
B.)
C.)
D.)
E.)

18. The first term is 1 for an = an-1 – 2. Find the third term.
iRespond Question
Fill-In F
403B2080-1CC DE1A223E4E
A.) -3;;
B.)
C.)
D.)
E.)

19. Ex: The first term is 1 for an = an-1 – 2. Find the next two terms.

20. Recursive Formula for Geometric Sequence

21. The first term is 320 for an = an-1 Find the next term. A.) -80;; B.)
iRespond Question
Fill-In F
2E6C59BB-017B-C344-BC20-96A452BFAE4A
A.) -80;;
B.)
C.)
D.)
E.)

22. The first term is 320 for an = an-1 Find the third term. A.) 20;; B.)
iRespond Question
Fill-In F
4310E593-BA89-AC4D-BEBD-947CA710FD87
A.) 20;;
B.)
C.)
D.)
E.)

23. Ex: The first term is 320 for an = -1/4 an-1. Find the next two terms.

24. Find the next term x y 1 3 2 13 23 4 33 n A.) 43;; B.) C.) D.) E.) F
iRespond Question F
Fill-In
1D87A3AE-F65A-CA4C-A x y 1 3 2 13 23 4 33 n
A.) 43;;
B.)
C.)
D.)
E.)

25. Find the next term and write the recursive rule.y 1 3 2 13 23 4 33 n

26. Find the next term x y 1 16 2 40 3 100 4 250 n A.) 625;; B.) C.) D.)
iRespond Question F
Fill-In
9616F E FA-39F289FD5ABB x y 1 16 2 40 3
100 4
250 n
A.) 625;;
B.)
C.)
D.)
E.)

27. Find the next term and write the recursive rule.y 1 16 2 40 3
100 4
250 n

28. Find the next term x y 1 2 14 3 98 4 686 n A.) 4802;; B.) C.) D.) E.)
iRespond Question F
Fill-In
1AC8100C-333F F7-99DFFA5B1A6C x y 1 2 14 3 98 4
686 n
A.) 4802;;
B.)
C.)
D.)
E.)

29. Find the next term and write the recursive rule.y 1 2 14 3 98 4
686 n

30. Find the next term x y 1 19 2 13 3 7 4 n A.) -5;; B.) C.) D.) E.) F
iRespond Question F
Fill-In
9F1BD1C0-5A AC F0B1A67 x y 1 19 2 13 3 7 4 n
A.) -5;;
B.)
C.)
D.)
E.)

31. Find the next term and write the recursive rule.y 1 19 2 13 3 7 4 n

32. Write the explicit rule and the recursive rule.
a1 = 15 and d = 5

33. Write the explicit rule and the recursive rule.
a1 = 4 and r = 0.2

34. Arithmetic and Geometric Sequences Practice 7 tables
Practice Worksheet
Arithmetic and Geometric Sequences Practice 7 tables

35. Explicit and Recursive Sequences Practice 12 problems
Homework
Explicit and Recursive Sequences Practice
12 problems