Numerical Patterns and Algebraic Rules Worksheet

Question 1

Complete the pattern and write the rule: 6, 12, 18, 24, __, __, __.

Accepted Answer

The missing numbers are 30, 36, and 42. The rule is to add 6 each time.

Question 2

Complete the pattern and write the rule: 81, 72, 63, 54, __, __, __.

Accepted Answer

The missing numbers are 45, 36, and 27. The rule is to subtract 9 each time.

Question 3

A rule says multiply the input by 4 and then add 1. Complete the table for inputs 1, 2, 3, 4, and 5.

Accepted Answer

The outputs are 5, 9, 13, 17, and 21. Each input is multiplied by 4, and then 1 is added.

Question 4

Look at the input-output pairs: 2 goes to 7, 4 goes to 9, 6 goes to 11, and 8 goes to 13. Write a rule that describes the pattern.

Accepted Answer

A rule is add 5 to the input. Each output is 5 more than its input.

Question 5

The rule is y = n + 8. Find y when n = 5, n = 10, and n = 25.

Accepted Answer

When n = 5, y = 13. When n = 10, y = 18. When n = 25, y = 33.

Question 6

The rule is y = 3n. Make a table for n = 1, 2, 3, 4, and 5.

Accepted Answer

The table values are 3, 6, 9, 12, and 15. The rule y = 3n means multiply each n value by 3.

Question 7

A growing pattern has 4 tiles in Figure 1, 7 tiles in Figure 2, 10 tiles in Figure 3, and 13 tiles in Figure 4. How many tiles will be in Figure 5 and Figure 6? Write the rule.

Accepted Answer

Figure 5 will have 16 tiles, and Figure 6 will have 19 tiles. The rule is to add 3 tiles for each new figure.

Question 8

Two patterns start at 0. Pattern A adds 5 each time. Pattern B adds 8 each time. Write the first five numbers in each pattern, including 0.

Accepted Answer

Pattern A is 0, 5, 10, 15, 20. Pattern B is 0, 8, 16, 24, 32.

Question 9

Use the two patterns from this rule: Pattern A starts at 2 and adds 3. Pattern B starts at 4 and adds 6. Write the first five terms of each pattern. What do you notice?

Accepted Answer

Pattern A is 2, 5, 8, 11, 14. Pattern B is 4, 10, 16, 22, 28. Each term in Pattern B is double the matching term in Pattern A.

Question 10

A number machine uses the rule input x 2 + 3. What are the outputs for inputs 4, 7, and 10?

Accepted Answer

The outputs are 11, 17, and 23. For each input, multiply by 2 and then add 3.

Question 11

Write an expression for this rule: Start with a number n, multiply it by 5, and subtract 2.

Accepted Answer

The expression is 5n - 2. This means five times the number n, minus 2.

Question 12

Evaluate the expression 6n + 4 when n = 2, n = 5, and n = 8.

Accepted Answer

When n = 2, the value is 16. When n = 5, the value is 34. When n = 8, the value is 52.

Question 13

A theater has 12 seats in the first row, 16 seats in the second row, 20 seats in the third row, and 24 seats in the fourth row. If the pattern continues, how many seats are in the sixth row?

Accepted Answer

The sixth row has 32 seats. The pattern adds 4 seats each row, so the fifth row has 28 seats and the sixth row has 32 seats.

Question 14

Points on a graph follow this rule: y = x + 2. List the ordered pairs for x = 0, 1, 2, 3, and 4.

Accepted Answer

The ordered pairs are (0, 2), (1, 3), (2, 4), (3, 5), and (4, 6). Each y-value is 2 more than the x-value.

Question 15

The pattern 5, 10, 20, 40, 80 follows a multiplication rule. What are the next two numbers, and what is the rule?

Accepted Answer

The next two numbers are 160 and 320. The rule is to multiply by 2 each time.

Numerical Patterns and Algebraic Rules

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