Patterns and Number Sequences — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. Inputs are 2, 4, 6, 8 and outputs are 7, 9, 11, 13. What is the rule?
A) Multiply by 3
B) Add 5
C) Add 3
D) Subtract 1
Compare each input to its output: 2 + 5 = 7, 4 + 5 = 9, 6 + 5 = 11, and 8 + 5 = 13. The same number, 5, is added every time, so the rule is add 5.
2. What rule makes the pattern 3, 9, 27, 81?
A) Add 6
B) Add 18
C) Multiply by 3
D) Multiply by 9
Each number is 3 times the one before: 3 × 3 = 9, 9 × 3 = 27, 27 × 3 = 81. The rule is multiply by 3.
3. In the pattern 1, 1, 2, 3, 5, 8, what comes next? Hint: add the last two numbers.
A) 10
B) 13
C) 11
D) 9
Each number is the sum of the two before it: 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8. So 5 + 8 = 13 comes next.
4. Starting from 2, which rule gives a larger 4th number: add 5 or multiply by 2?
A) Add 5 gives 17
B) Multiply by 2 gives 16
C) They are equal
D) Add 5 gives 20
Add 5 four times to 2: 2, 7, 12, 17. Multiply by 2 four times from 2: 2, 4, 8, 16. Wait — start counts as the 1st number, so the 4th by adding 5 is 17 and by doubling is 16. Doubling grows much faster overall, but here the 4th term using add 5 is 17 and using multiply by 2 is 16, which means the multiply rule gives 16. Among the choices, multiply by 2 gives 16 is the matching correct fact.
Part B: Fill in the Blank
Write the correct answer on each line.
1. In the pattern 5, 10, 20, 40, each number doubles. The next number is 80.
Each number doubles: 5, 10, 20, 40. Doubling 40 gives 80, so the next number is 80.
2. An input-output table uses multiply by 4. If the input is 7, the output is 28.
Multiply the input by 4: 7 × 4 = 28, which is the output.
3. The pattern 11, 22, 33, 44, 55 is missing the number 44.
The pattern counts by 11s: 11, 22, 33, 44, 55. The number that fits between 33 and 55 is 44.
4. In the pattern 96, 48, 24, 12, each number is divided by 2.
Each number is half of the one before: 96, 48, 24, 12. Half means dividing by 2, so the rule is divide by 2.
5. The 9th number when counting by 6 is 54.
Counting by 6 gives 6, 12, 18, 24, 30, 36, 42, 48, 54. The 9th number is 6 × 9 = 54.