Patterns and Number Sequences — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. What comes next in 8, 16, 24, 32, 40?
These are multiples of 8 in order, meaning the rule is add 8. Adding 8 to the last number, 32, gives 40.
2. The pattern 55, 50, 45, 40 follows the rule subtract 5. The next number is 35.
Each step shrinks by 5 (55, 50, 45, 40), and taking 5 from 40 gives 35. The constant drop of 5 confirms the rule is subtract 5.
3. An input-output table uses the rule multiply by 3. If the input is 8, the output is 24.
Multiply the input 8 by 3 to follow the table's rule. 8 times 3 equals 24, so the output is 24.
4. The rule for the pattern 5, 13, 21, 29 is add 8.
Subtract neighbors to find the gap: 13 minus 5 is 8, and 21 minus 13 is also 8. That steady jump of 8 means the rule is add 8.
5. In the pattern 3, 9, 27, 81, each number is multiplied by 3.
3 times 3 is 9, 9 times 3 is 27, and 27 times 3 is 81. Each number is tripled, so the rule is multiply by 3.
6. If the rule is subtract 8 and the input is 40, the output is 32.
Apply the rule by taking 8 away from 40. Since 40 minus 8 equals 32, the table's output is 32.
7. In the pattern 12, 24, 36, 48, the missing number is 24.
Look at the known numbers: 36 minus 12 equals 24, and 48 minus 36 equals 12. The pattern adds 12 each time, so the missing second number is 12 plus 12, which is 24.
8. What comes next in 75, 68, 61, 54, 47?
The pattern shrinks by 7 each step (75, 68, 61, 54). Subtracting 7 from 54 gives 47 as the next number.
9. In the repeating pattern 2, 5, 8, 2, 5, 8, 2, the next number is 5.
The group 2, 5, 8 repeats, and the third group has already started with 2. The next spot in the group is 5.
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 7, input = 13
→ 20
24
Rule: multiply by 6, input = 4
→ 24
20
Rule: subtract 11, input = 50
→ 39
39
Rule: add 15, input = 10
→ 25
25
Correct matches: Rule: add 7, input = 13 → 20; Rule: multiply by 6, input = 4 → 24; Rule: subtract 11, input = 50 → 39; Rule: add 15, input = 10 → 25.