Sequences, Patterns, and Tables
Sequences
Input and Output
Order of OPerations
Equations with Multiple Operations
100

Describe the pattern in 15, 12, 9, 6, . . . . Then find the next three terms in the sequence.

Start with 15 and add −3 repeatedly. The next three terms are 3, 0, and −3.

100
What do we call an ordered arrangement of terms that make up a pattern?
Sequence
100
Write an equation that describes the pattern in the table. Input (x) : 5 9 13 17 Output (y): 9 13 17 21
x + 4 = y
100
What is the first operation we should solve when using the order of operation?
Solve inside the parenthesis
100
If we were to try to solve this equation what is the first thing we should do? n = 1 (n x 3) + 5 = y
Substitute the n with 1. (1 x 3) + 5 = y
200

Describe the pattern in 2, −8, 32, −128 . . . . Then find the next three terms in the sequence.

Start with 2 and multiply by −4 repeatedly. The next three terms are 512, −2,048, 8,192, .

200
What do we call each number in a numeric pattern?
Term
200
Write an equation that describes the pattern in the table. Input (x) : 11 16 21 26 output(y): 2 7 12 17
x - 9 = y
200
What are the steps for the order of operations?
1. solve inside of the parenthesis 2. multiply and divide 3. add and subtract
200
If n = 2, what will m equal? (5 + n) x 4 = m
m = 28
300
64, 55, 46, 37, 28, 19 What is the rule for this pattern?
subtract 9
300
Rule: add 8 5, __, __, __, __ What are the next four terms in this sequence?
13, 21, 29, 37
300
Use the rule to find the next output number. rule: f + 3 = h input: 3 6 9 12 output: 6 9 12 ?
15
300
What is the first thing we should solve in this equation? ( 2+1) x 3
parenthesis (2 + 1) x 3 V 3 x 3
300
Complete the table. (x -1) + 2 = y input (x) : 1 2 3 4 output(y) : 2 3 ? ?
4 , 5
400
53, 49, 52, 48, 51, 47 Extend the pattern. What will the next two terms be?
50, 46
400
Rule: multiply by 2 3, __, __, __, __ Fill in the next four terms and make an observation.
6, 12, 24, 48 All of the terms are multiples of 8. The terms are increasing.
400
Write an equation that describes the pattern in the table. input (j) : 1 2 3 4 output (k): 2 4 6 8
j x 2 = k
400
Solve this equation. 5 + 9 x 3 = ?
32
400
Complete the table. (5 x j ) + 5 = k input (j) : 1 2 3 4 output (k) : 10 15 ? ?
20 , 25
500
Leela practices basketball everyday in her driveway. Each day, her goal is to make 4 more baskets than she had made the day before. If she makes 10 baskets on the first day how many baskets will she make on the 7th day?
34 baskets
500
On Monday, a toy store sold 4 race cars. On Tuesday, it sold 8 race cars.On Wednesday it sold 16 race cars. If this pattern continues how many cars will be sold on Friday?
64 race cars
500
Find the rule and use it to find the next output number. input (l) : 10 15 20 25 output(m) : 2 3 4 ?
5
500
Solve this equation. (4 + 20) - 2 x 5 = ?
14
500
Mauricio hits a baseball 4 times as often as Tony each game. He also hits 20 baseballs every Monday after practice. How many baseballs will Mauricio hit this week if Tony hits 4 baseballs at the game on Saturday?
( 4 x 4) + 20 = 36
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