1. Patterns and Sequences
AIMS Math Review – Spring, 2008

2. Period 1: Patterns Determine the next item in the pattern. 1. 2. 3.
n = n = n = n = 4

3. Period 1: Patterns ANSWERS
Determine the next item in the pattern. 1. 2. 3.
n = n = n = n = n = 5

4. Period 2 Find the missing terms in the sequences.
1, 4, 9, 16, 25, _____, 49, 64, ____, 100
32, 16, ___, 4, 2, ___, ½, ___
1, 3, 9, ____, 81, ____
2, 9, 16, ___, 30, 37, 44, ___, 58
19, 17, 15, 13, ___, 9, 7, 5, 3, ___

5. Period 2 ANSWERS Find the missing terms in the sequences.
1, 4, 9, 16, 25, _36_, 49, 64, _ 81 _, 100 (perfect squares)
32, 16, _ 8 _, 4, 2, _ 1 _, ½, _ ¼ _ (divide by 2)
1, 3, 9, _ 27 _, 81, _243 _ (multiply by 3)
2, 9, 16, _ 23 _, 30, 37, 44, _ 51_, 58 (add 7)
19, 17, 15, 13, _ 11__, 9, 7, 5, 3, _ 1__ (subtract 2)

6. Period 3 Find the next three terms in the sequence. 9, 6, 3, 0, -3, …
9, 6, 3, 0, -3, …
3, -6, 12, -24, …
21, 18, 15, 12, …
1, 3, 6, 10, 15, 21, …
100, 99, 97, 94, 90, …

7. Period 3 ANSWERS Find the next three terms in the sequence.
9, 6, 3, 0, -3, … …-6, -9, -12 (subtract 3)
3, -6, 12, -24, … …48, -96, 192 (multiply by -2)
21, 18, 15, 12, … …9, 6, 3 (subtract 3)
1, 3, 6, 10, 15, 21, … … 28, 36, 45 (add one more than the previous (add 2, then add 3, then add 4, …)
100, 99, 97, 94, 90, … …85, 79, 72 (subtract one more than the previous (subtract 1, then subtract 2, then subtract 3, …)

8. Period 4
The first row in a theater has 15 seats, the second row has 17 seats, and the third row has 19 seats. If this pattern continues, how many seats will the 8th row have?
Count the number of triangles in each figure. How many triangles will a 15-sided figure have?

9. Period 4 ANSWERS
The first row in a theater has 15 seats, the second row has 17 seats, and the third row has 19 seats. If this pattern continues, how many seats will the 8th row have? 29 seats (Row 4 = 21, Row 5 = 23, Row 6 = 25, Row 7 = 27…)
Count the number of triangles in each figure. How many triangles will a 15-sided figure have? 13 (the number of triangles is 2 less than the number of sides of a convex polygon)

10. Period 5
What will be the next in the pattern? 1. 2. 3. 4.

11. Period 5 ANSWERS What will be the next in the pattern? 1. 2. 3. 4.
12 sides

12. Period 6
A Fibonacci-like sequence is one in which previous values are added to get the next number in a sequence. Determine the next three terms in each Fibonacci-like sequence.
1, 1, 2, 3, 5, 8, …
1, 2, 3, 6, 11, 20, …
5, 7, 12, 19, 31, …
0, 1, 1, 2, 4, 7, 13, …

13. Period 6 ANSWERS
A Fibonacci-like sequence is one in which previous values are added to get the next number in a sequence. Determine the next three terms in each Fibonacci-like sequence.
1, 1, 2, 3, 5, 8, … …13, 21, 34
1, 2, 3, 6, 11, 20, … …37, 68, 125
5, 7, 12, 19, 31, … …50, 81, 131
0, 1, 1, 2, 4, 7, 13, … …24, 44, 81