Patterns and Number Sequences — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. The pattern 4, 11, 18, 25 follows the rule add 7.
Find the difference between any two side-by-side numbers: 11 minus 4 is 7, and 18 minus 11 is 7. The same gap of 7 appears every step, so the rule is add 7.
2. What comes next in 9, 18, 27, 36, 45?
These are the multiples of 9 counting upward. Adding 9 to the last number, 36, gives 45 as the next number in the sequence.
3. The pattern 70, 63, 56, 49 follows the rule subtract 7.
The numbers shrink each step: 70 minus 63 is 7, and 63 minus 56 is also 7. Because the gap is always 7 going down, the rule is subtract 7.
4. An input-output table uses the rule multiply by 4. If the input is 5, the output is 20.
Multiply the input 5 by 4 to follow the rule. 5 times 4 equals 20, so 20 is the number the table gives as the output.
5. In the pattern 2, 4, 8, 16, each number is multiplied by 2.
Each number is double the one before it: 2 times 2 is 4, 4 times 2 is 8, and 8 times 2 is 16. Doubling means you multiply by 2 every time.
6. If the rule is add 11 and the input is 9, the output is 20.
Follow the rule by adding 11 to the input 9. Since 9 plus 11 equals 20, the output is 20.
7. In the pattern 15, 30, 45, 60, the missing number is 30. The rule is add 15.
With 30 filling the gap, the pattern reads 15, 30, 45, 60. Each step rises by 15, so the rule is add 15.
8. What comes next in 84, 77, 70, 63, 56?
The sequence drops by 7 each step: 84, 77, 70, 63. Subtracting 7 from 63 gives 56 as the next number.
9. In the repeating pattern 4, 8, 12, 4, 8, 12, the next number is 4.
The group 4, 8, 12 repeats over and over. Two full groups have finished, so the next number starts a third group with 4.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
Rule: add 6, input = 14
→ 20
30
Rule: subtract 9, input = 45
→ 36
20
Rule: multiply by 5, input = 6
→ 30
36
Rule: add 13, input = 8
→ 21
21
Correct matches: Rule: add 6, input = 14 → 20; Rule: subtract 9, input = 45 → 36; Rule: multiply by 5, input = 6 → 30; Rule: add 13, input = 8 → 21.