Activities

1. Describe, in words, the pattern found in the sequence of numbers below.

72        109           146             183             220

2. What is the 7^th number in the sequence below?

-1, 6, 13, …

3. Write an expression that can be used to create the following sequence.

5, 3, 1, -1, …

4. Fill in the table below based on the graph, then write an expression that could be used to find the nth term of the sequence.

5. If the initial value of a sequence of numbers is -5 and the difference between any two consecutive terms is 7, write an expression to find the n^th term of the sequence. What are the 7^th , 10^th, and 100^th terms in this sequence?

6. What is the pattern in the following numbers: 1, 1, 2, 3, 5, 8, 13, 21, …?

7. What is the n^th term in the following sequence:  5, 8.5, 12, 15.5, …?

8. How many squares are in the 25^th figure?

9. Determine the next three terms in this sequence.

7, 11, 16, 22, 29, ____, _____, _____

10. Represent the following pattern on the graph below, then write an expression that could determine the n^th term of the sequence.

9, 5, 1, -3, -7

11. Jeff is trying to memorize the digits of π. On his first five tries he memorizes 14, 17, 20, 23, and 26 digits respectively. If he continues memorizing at this rate, how many digits of π will Jeff know by his 20^th try?

12. Which of the following sequences are linear?

1. 5, 10, 15, 20, …
2. 8, 6, 5, 4.5, …
3. -2, -7, -12, -17, …
4. 5, 5, 5, 5, …
5. π, 2π, 3π, …

13. Joanna bought a new car for $37,999. If the car’s depreciation (loss of value) occurs at $500 per month for the first year, write an expression that determines the value after n months. What is the car’s value after 1 year?

14. Write down the first 7 numbers represented by the sequence 4(2 – x).

15. Taja rented a canoe for 7 hours and paid $23.25. Steven rented a canoe for 5 hours and paid $18.75. Using this information, create a list of the cost to rent the canoe for any hour amount from zero to ten.

16. Fill in the banks in the linear pattern below.

21, ____, _____, -30

17. Write an expression that can be used to describe the difference between the n^th and (n +1)^st number in this sequence.

3, 6, 11, 18, 27, …

18. Write an expression that could be used to determine the n^th term in this pattern.  

19. Write an expression that would be used to find the n^th term of this sequence.

3, 5, 9, 17, 33, 65, …

20. What is the smallest positive integer that is part of the following sequence?

…, 534, 538.5, 543, 547.4, 552, …

21. The sum of three consecutive numbers in the following sequence is 117, what is the first of the three numbers?

0, 3, 6, 9, …

22. Write the pattern and expression that are created when a cube’s side lengths increase by 1 unit for every n^th term in the pattern, starting at n = 1.

23. Two patterns are described as follows:

Pattern 1:  2, 9, 16, 23, …
Pattern 2:  4, 7, 10, 13, …

What is the expression that is created when you make a new pattern by subtracting each term in pattern 2 from pattern 1?

24. A group of buckets are stacked inside one another according to the graph shown below, what is the height, in inches, of 1 bucket?

25. What are the next three terms in this sequence?

4, 6, 9, 14, ___, ____, ____

Answer Key/Rubric

1. The initial value is 72 and each term increases by 37

2. 41

3. 7 – 2x

4. Expression: 2x – 1
   

5. 7n – 5, 44, 65, 695

6. Any term is the sum of the two previous terms

7. 3.5n + 1.5

8. 101 squares

9. 37, 46, 56

10. Expression:  13 – 4n

11. 71 digits

12. a, c, d, and e

13. 37,999 – 500n , after 1 year the car will be valued at $31,999

14. 4, 0, -4,-8, -12, -16, -20

16. 21, 4, -13, -30

17. (2n – 1)

19. 2ⁿ + 1

20. 3

21. 36

22. 1, 8, 27, 64, 125, … Expression: n³

23. 4n – 6

24. 3.5 inches

25. 4, 6, 9, 14, 22, 35, 56