Patterns and Number Sequences — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. Inputs are 3, 5, 7, 9 and outputs are 10, 14, 18, 22. What is the rule?
A) Add 7
B) Multiply by 2 and add 4
C) Multiply by 3
D) Add 9
Test the rule with the first input: 3 times 2 is 6, plus 4 is 10 -- that matches the output. Check another: 5 times 2 is 10, plus 4 is 14, which also matches.
2. What rule makes the pattern 2, 6, 18, 54?
A) Add 4
B) Multiply by 2
C) Multiply by 3
D) Add 12
Each number is tripled to get the next: 2 times 3 is 6, 6 times 3 is 18, and 18 times 3 is 54. The rule that keeps working is multiply by 3.
3. In the pattern 1, 2, 4, 7, 11, what comes next? Hint: the amount added grows by 1 each time.
A) 14
B) 16
C) 15
D) 13
The jumps grow: +1, +2, +3, +4. The next jump should be +5, and 11 plus 5 equals 16.
4. Starting from 3, which rule gives a larger 5th number: add 4 or multiply by 2?
A) Add 4 gives 19
B) Multiply by 2 gives 48
C) They are equal
D) Add 4 gives 23
Add 4 gives 3, 7, 11, 15, 19 so the 5th number is 19. Multiply by 2 gives 3, 6, 12, 24, 48 so the 5th number is 48, which is much larger.
Part B: Fill in the Blank
Write the correct answer on each line.
1. In the pattern 4, 8, 16, 32, each number doubles. The next number is 64.
Doubling means multiplying by 2. The last number is 32, and 32 times 2 equals 64.
2. An input-output table uses multiply by 5. If the input is 9, the output is 45.
Multiply the input 9 by 5 to follow the rule. 9 times 5 equals 45, so 45 is the output.
3. The pattern 13, 26, 39, 52, 65 is missing the number 52.
The pattern counts by 13s: 13, 26, 39, then the gap, then 65. Adding 13 to 39 gives 52, and 52 plus 13 gives 65, so 52 fits perfectly.
4. In the pattern 200, 100, 50, 25, each number is divided by 2.
Each number is half the one before it: 200 halved is 100, 100 halved is 50, and 50 halved is 25. Halving means dividing by 2.
5. The 7th number when counting by 9 is 63.
Counting by 9 means multiplying 9 by the position number. The 7th spot is 9 times 7, which equals 63.