Arithmetic Sequence— goes from one term to the next term by always adding or _____________________ the same value. We call this the common __________________________.Geometric Sequence— goes from one term to the next term by always multiplying or __________________ by the same value. We call this the common _________________.

Math-7 NOTES DATE: ______/_______/_______What: sequences Why: To identify the common difference or ratio in a sequence and determine whether or not the sequence is arithmetic, geometric, or neither.What: sequences Why: To identify the common difference or ratio in a sequence and determine whether or not the sequence is arithmetic, geometric, or neither.

NAME:

Sequence Rule

(CommonDiff. or Ratio)

WhatComes next?

Arithmeticor

Geometric?

VariableExpressio

n

1) -5, 3, 11, 19 . . .

2) 5, 10, 20, 40 . . .

3) 16, 10, 4, -2 . . .

4) 80, 20, 5, 5/4 . . .

5) 1, 2, 4, 7, 11 . . .

6) 1/9, 3/9, 1, 3 . . .

7) 1, 1, 2, 2, 3, 3 . . .

8) 1, -3, 9, -27 . . .

9) 1/10, 3/10, 5/10 . . .

10) 1, 1, 2, 3, 5, 8, 13 . . .

3) Which of the following sequences is a geometric sequence?A. 27, 9, 3, 1 . . .B. 1, 2, 6, 24. . .C. 2, 4, 6, 8 . . .4) What would be the 7th term of the following arithmetic sequence?1, 4, 7, 10 . . . A. 13B. 19C. 22

5) Which of the following sequences is neither a geometric nor an arithmetic sequence?A. 10, 20, 30, 40 . . .B. 1, 2, 3, 2, 4, 2, 5, 2, . . .C. 1/10, 2/10, 3/10 . . .6) What is the common difference in the following arithmetic sequence?10, 6, 2, -2 . . .A. 4B. -4C. ¼

7) What is the common ratio in the following geometric sequence?1, -2, 4, -8, 16 . . . A. -2B. 2C. ½

8) Which variable expression describes the relationship between any two consecutive terms in the following sequence? -1, 4, -16, 64 . . . A. 4nB. -4nC. n¼

9) Which variable expression describes the relationship between any two consecutive terms in the following sequence? -12, -4, 4, 12, 20 . . . A. n – 4B. 4nC. n + 4

10) What is the common ratio in the following geometric sequence?88, 44, 22, 11, 11/2 . . .

A. 2B. ½C. - ½

1) Which of the following sequences is an arithmetic sequence?A. 3, 9, 27 . . .B. 1, 3, 6, 10, 15 . . .C. 52, 49, 46, 43 . . .2) What would be the 5th term of the following geometric sequence?1, 5, 25 . . .A. 125B. 625C. 30

Multiple Choice:

DATE: ______/_______/_______NAME:__________________________Math- 7 PRACTICE

“sequences”For the following sequences, describe the “rule” AND identify the next term:

13. What is the 8th term in the following sequence?3, 9, 27, 81, 243, 729 . . .

14. What is the 6th term of the geometric sequence shown? 80, 40, 20 . . .

15. What is the common difference of the arithmetic sequence shown?-5, -1, 3, 7 . . .

16. What is the common ratio of the geometric sequence shown?729, 243, 81, 27, 9 . . .

17. Write a variable expression that can be used represent the relationship between two consecutive terms of the following sequence:

8, 12, 16, 20 . . .

18. What is the missing tem in this sequence? 1, 5, 25, ____, 625, ….

1) 6, 12, 18, 24,… _____ 2) 1, 4, 16, 64, … _____ 3) 72, 36, 18, 9,…_____

4) 9, 18, 27, 36, 45,…_____ 5) 0.2, 0.4, 0.8, 1.6,…_____ 6) 1, 3, 9, 27,…_____

7) 0, 16, 32, 48, 64…._____ 8) 1.2, 2.3, 3.4, 4.5, …._____

9) 3, 7, 11, 15…._____

10) 128, 32, 8, 2, …._____ 11) 2 , -6, 18, -54,…_____ 12) 7, 7, 7, 7,…______

DATE: ______/_______/_______NAME:__________________________

Math- 7 PRACTICE “sequences”

Match each sequence with the variable expression that describes the relationship between the consecutive terms of the sequence.

13. Which of the above problems are arithmetic sequences? _________________________

14. Which of the above problems are geometric sequences? _________________________

1. ____ 2, 4, 6, 8, 10, … A. n + 10

2. ____ 1, 3, 9, 27, 71 B. 1/3 n

3. ____ 45, 41, 37, 32, 29, …. C. 0.2n

4. ____ 11, 21, 31, 41, 51, …. D. n + 5

5. ____ 10, 5, 2.5, 1.25, 0.625, …. E. n + 2

6. ____ 11, 3, -5, -13, -21, …. F. 0.5n

7. ____ 100, 20, 4, 0.8, 0.16,….. G. n + (-2)

8. ____ 7, 10.5, 15.75, 23.625, 35.4375, ….. H . n + (-4)

9. ____ 36, 12, 4, 1.333, …. I. 1.5n

10. ____ -3, -6, -12, -24, -48, J. 3n

11. ____ -80, -75, -70, -65, -60, …. K. n + (-8)

12. ____ 1, -1, -3, -5, …. L. 2n