Patterns and Number Sequences — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. What is the rule for the pattern 2, 5, 11, 23?
A) Add 3 each time
B) Double and add 1
C) Multiply by 2
D) Add 6 each time
Test the rule: 2 doubled is 4, plus 1 is 5. Then 5 doubled is 10, plus 1 is 11. And 11 doubled is 22, plus 1 is 23. "Double and add 1" works every time.
2. An input-output table uses multiply by 4. Which input gives an output of 36?
A) 8
B) 9
C) 7
D) 6
Work backward by dividing the output 36 by the rule number 4. Since 36 divided by 4 equals 9, the input must have been 9.
3. What comes next in the pattern 243, 81, 27, 9?
A) 1
B) 6
C) 3
D) 0
Each number is divided by 3 to get the next one: 243 divided by 3 is 81, 81 divided by 3 is 27, and 27 divided by 3 is 9. Dividing 9 by 3 gives 3.
4. In the pattern 4, 8, 12, 16, 20, 24, what is the 9th number?
A) 32
B) 40
C) 36
D) 28
The pattern counts by 4s, so any position times 4 gives that number. The 9th position is 9 times 4, which equals 36.
Part B: Fill in the Blank
Write the correct answer on each line.
1. In the pattern 3, 6, 12, 24, 48, each number doubles. The next number is 96.
Doubling means multiplying by 2 each step. The last number is 48, and 48 times 2 equals 96.
2. If the rule is subtract 9 and the input is 63, the output is 54.
Follow the rule by taking 9 away from 63. Since 63 minus 9 equals 54, the table's output is 54.
3. In the multiplication table, the row for 7 shows 7, 14, 21, 28. The next number is 35.
The row for 7 lists 7 times 1, 7 times 2, and so on. After 28 (which is 7 times 4), the next product is 7 times 5, which equals 35.
4. The pattern 90, 78, 66, 54, 42 follows the rule subtract 12.
Check the drop between numbers: 90 minus 78 is 12, and 78 minus 66 is also 12. The same gap of 12 appears every step, so the rule is subtract 12.
5. In the pattern 5, 15, 45, 135, the missing number is 45.
Each number is multiplied by 3 to get the next: 5 times 3 is 15, and 15 times 3 is 45. You can also check backward: 135 divided by 3 is 45.