Patterns and Number Sequences — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. In the pattern 1, 3, 7, 15, what is the rule?
A) Add 2 each time
B) Double and add 1
C) Multiply by 3
D) Add 4 each time
Look at each step: 1 doubled is 2 plus 1 makes 3, 3 doubled is 6 plus 1 makes 7, 7 doubled is 14 plus 1 makes 15. The rule is double and add 1.
2. An input-output table uses multiply by 3. Which input gives an output of 27?
A) 6
B) 8
C) 9
D) 7
Multiplying by 3 gives 27 when the input is 9, since 9 × 3 = 27.
3. What comes next in the pattern 64, 32, 16, 8?
A) 6
B) 2
C) 4
D) 0
Each number is half of the one before: 64 to 32, 32 to 16, 16 to 8. Half of 8 is 4, so the next number is 4.
4. In the pattern 5, 10, 15, 20, 25, 30, what is the 8th number?
A) 35
B) 45
C) 40
D) 50
The pattern counts by 5s, so the 8th number is 5 × 8 = 40.
Part B: Fill in the Blank
Write the correct answer on each line.
1. In the pattern 2, 6, 18, 54, each number is multiplied by 3. The next number is 162.
Each number is multiplied by 3: 2, 6, 18, 54. Then 54 × 3 = 162, which is the next number.
2. If the rule is subtract 7 and the input is 50, the output is 43.
Subtract 7 from the input of 50: 50 − 7 = 43.
3. In the addition table, the row for 8 shows 8, 16, 24, 32. The next number is 40.
The row counts by 8s: 8, 16, 24, 32. Adding 8 to 32 gives 40.
4. The pattern 100, 85, 70, 55, 40 follows the rule subtract 15.
From 100 to 85 is a drop of 15, and the same drop of 15 happens between 85 and 70, 70 and 55, and 55 and 40. The rule is subtract 15.
5. In the pattern 4, 12, 36, 108, the missing number is 36.
Each number is multiplied by 3: 4 × 3 = 12, and 36 × 3 = 108. So the missing number between 12 and 108 is 12 × 3 = 36.