Patterns & Rules
What comes next? 2, 4, 6, 8, ___, ___
10, 12
Input 3 → Rule: ×2 → Output = ?
6
Solve: x + 6 = 10
4
A pizza costs $12. How much for 3 pizzas? (Write as an equation)
12x → for 3 pizzas = $36
Fill the table (rule?): n=1 → 4, n=2 → 7, n=3 → 10
Rule = 3n + 1
Rule for the pattern: 5, 10, 15, 20, ___
Input 7 → Rule: ×4 – 1 → Output = ?
27
Solve: 3x = 21
7
A farmer packs eggs in boxes of 12. She sells x boxes and has 72 eggs. Solve for x.
12x = 72 → x = 6
What is the rule for the sequence: 3, 6, 9, 12…?
Rule = 3n
A pattern starts at 3 and goes +5 each time. What is the 10th number?
48
Fill in the missing outputs: (Rule: ×3 + 2) → Inputs: 2, 5, 8
8, 17, 26
Solve: 2x + 5 = 19
7
A bus has 50 seats. Each row has 5 seats. How many rows?
10 rows
If the rule is 2n + 1, what is the 10th term?
n = 21
A shape pattern has 4 triangles in step 1, 8 in step 2, 12 in step 3. How many in step 7?
28
A machine doubles the input, then subtracts 5. What is the output if input = 12?
19
Solve: x – 9 = 34
43
A phone plan costs $10 + $3 per gigabyte. Write the equation for g gigabytes.
C = 10 + 3g
A pattern grows: n=1 → 5, n=2 → 11, n=3 → 17. Write the rule.
Rule = 6n – 1
A pattern doubles each time. Step 1 = 2. How many at Step 8?
256
If the output is 41 and the rule is (×5 – 4), what was the input?
9
Sam has x marbles. He buys 8 more and now has 25. Write and solve the equation
x + 8 = 25 → x = 17
A concert ticket costs $25 plus $2 per service fee. Write the equation and find the cost for 7 tickets
C = 25n + 2n = 27n; for 7 tickets = $189
Using the rule 4n + 2, what is the value when n=50?
n = 202