Patterns and Number Sequences — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
The next number in 25, 30, 35, 40 is 50.
Corrected: The next number in 25, 30, 35, 40 is 45.
Each number jumps up by 5, so adding 5 to 40 gives 45. Jumping all the way to 50 would mean adding 10, which breaks the pattern.
2. Fix the sentence:
The pattern 10, 8, 6, 4 uses the rule add 2.
Corrected: The pattern 10, 8, 6, 4 uses the rule subtract 2.
These numbers shrink from 10 down to 4, so the rule must subtract instead of add. Each step takes away 2, so the corrected rule is subtract 2.
3. Fix the sentence:
The pattern 9, 12, 15, 18 continues with 22.
Corrected: The pattern 9, 12, 15, 18 continues with 21.
Every step adds 3 (9, 12, 15, 18), so adding 3 to 18 lands on 21. Jumping to 22 would be adding 4, which is not how this pattern grows.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The pattern 14, 21, 28, 35 follows the rule add 7.
Take any two numbers next to each other and find the difference: 21 minus 14 is 7, and 28 minus 21 is also 7. The same gap of 7 repeats, so the rule is add 7.
2. What comes next in 40, 36, 32, 28, 24?
The numbers shrink by 4 each step (40, 36, 32, 28). Taking 4 away from 28 leaves 24 as the next number in the sequence.
3. In the repeating pattern A, B, B, A, B, B, the next letter is A.
The pattern repeats in groups of A-B-B, and two full groups have already finished. The next letter starts a brand new group, so it must be A.
4. An input-output table uses the rule subtract 4. If the input is 20, the output is 16.
Apply the rule by taking 4 away from the input number 20. Since 20 minus 4 equals 16, the output the table produces is 16.
Part C: True or False?
Read each statement. Circle True or False.
1. The pattern 6, 9, 12, 15, 18 uses the rule add 3.
True False
The gaps between numbers are 9-6=3, 12-9=3, 15-12=3, and 18-15=3. The same gap of 3 shows up between every pair, confirming that the rule is add 3.
2. If the input is 5 and the rule is add 10, the output is 20.
True False
Adding 10 to 5 gives 15, not 20. To reach 20 from 5 you would have to add 15, so the statement is false.
3. In a growing pattern, each number is larger than the one before it.
True False
The word "growing" means getting bigger, which happens whenever the rule adds or multiplies. Each new number ends up larger than the one before it.