Number Pattern Worksheets - Free Printable
Educational worksheet: Number Pattern Worksheets. Download and print for classroom or home learning activities.
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Show Answer Key & Explanations
Step-by-step solution for: Number Pattern Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Number Pattern Worksheets
Let’s solve each number pattern step by step. We’ll look at the numbers given and figure out what rule is being used — like adding or subtracting the same amount each time, or counting by 2s, 5s, etc.
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Problem 1: 1, __, __, 4, 5, __, __, 8
Look at the known numbers:
After 1 comes 4 → that’s +3 over two steps? Wait — let’s check from 4 to 5: that’s +1. Then 5 to 8 is +3 over two steps? Hmm.
Actually, let’s list positions:
Position: 1 2 3 4 5 6 7 8
Numbers: 1 ? ? 4 5 ? ? 8
From position 4 (number 4) to position 5 (number 5): +1
From position 5 (5) to position 8 (8): that’s 3 steps later → 5 to 8 is +3 → so maybe +1 per step?
Check: If we go +1 each time:
1, 2, 3, 4, 5, 6, 7, 8 → YES! That fits perfectly.
So missing numbers: 2, 3, 6, 7
✔ Problem 1: 1, 2, 3, 4, 5, 6, 7, 8
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Problem 2: 34, __, __, 37, 38, __, 40, __
Known: 34, then later 37, 38, 40
From 34 to 37: that’s +3 over 3 steps? Let’s count positions:
Pos: 1=34, 2=?, 3=?, 4=37, 5=38, 6=?, 7=40, 8=?
From pos 4 (37) to pos 5 (38): +1
From pos 5 (38) to pos 7 (40): that’s 2 steps → +2 → so likely +1 per step.
Try counting up by 1:
34, 35, 36, 37, 38, 39, 40, 41 → perfect!
Missing: 35, 36, 39, 41
✔ Problem 2: 34, 35, 36, 37, 38, 39, 40, 41
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Problem 3: __, 4, 6, __, 10, __, 14, __
Given: 4, 6, 10, 14
Look at differences:
6 - 4 = 2
10 - 6 = 4 → not consistent? Wait — maybe it’s increasing by 2 each time?
Wait: 4, 6 → +2
Then next should be 8? But it says blank, then 10 → yes! So if we assume +2 each time:
Start before 4: 4 - 2 = 2 → first blank is 2
Then: 4, 6, 8, 10, 12, 14, 16
Check positions:
Pos: 1=?, 2=4, 3=6, 4=?, 5=10, 6=?, 7=14, 8=?
If sequence is even numbers starting at 2:
2, 4, 6, 8, 10, 12, 14, 16 → matches all given!
Missing: 2, 8, 12, 16
✔ Problem 3: 2, 4, 6, 8, 10, 12, 14, 16
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Problem 4: 5, 10, __, __, 25, __, 35, __
Given: 5, 10, ..., 25, ..., 35, ...
Looks like multiples of 5?
5, 10, 15, 20, 25, 30, 35, 40 → yes!
Check:
Pos: 1=5, 2=10, 3=?, 4=?, 5=25, 6=?, 7=35, 8=?
So: 5, 10, 15, 20, 25, 30, 35, 40
Missing: 15, 20, 30, 40
✔ Problem 4: 5, 10, 15, 20, 25, 30, 35, 40
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Problem 5: 18, __, __, 24, 26, __, 30, __
Given: 18, ..., 24, 26, ..., 30, ...
Look at 24 to 26: +2
26 to 30: that’s +4 over 2 steps? Maybe +2 each time?
Try: Start at 18, add 2 each time:
18, 20, 22, 24, 26, 28, 30, 32 → perfect!
Positions:
1=18, 2=?, 3=?, 4=24, 5=26, 6=?, 7=30, 8=?
So: 18, 20, 22, 24, 26, 28, 30, 32
Missing: 20, 22, 28, 32
✔ Problem 5: 18, 20, 22, 24, 26, 28, 30, 32
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Problem 6: 56, __, 58, __, __, __, 62, 63
Given: 56, ?, 58, ?, ?, ?, 62, 63
Notice last two: 62, 63 → +1
Before that: 58 to 62 is 4 steps? Let’s map positions:
Pos: 1=56, 2=?, 3=58, 4=?, 5=?, 6=?, 7=62, 8=63
From pos 7 to 8: +1 → so probably counting up by 1.
Try full sequence: 56, 57, 58, 59, 60, 61, 62, 63 → yes!
Missing: 57, 59, 60, 61
✔ Problem 6: 56, 57, 58, 59, 60, 61, 62, 63
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Problem 7: 60, __, __, 75, __, 85, 90, __
Given: 60, ..., 75, ..., 85, 90, ...
Look at 85 to 90: +5
75 to 85: that’s 2 steps? From pos 4=75 to pos 6=85 → 2 steps → +10 → so +5 per step?
Try: Count by 5s starting at 60:
60, 65, 70, 75, 80, 85, 90, 95 → perfect!
Positions:
1=60, 2=?, 3=?, 4=75, 5=?, 6=85, 7=90, 8=?
So: 60, 65, 70, 75, 80, 85, 90, 95
Missing: 65, 70, 80, 95
✔ Problem 7: 60, 65, 70, 75, 80, 85, 90, 95
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Problem 8: __, 40, 42, __, 46, __, 50, __
Given: 40, 42, ..., 46, ..., 50, ...
40 to 42: +2
42 to 46: that’s 2 steps? Pos 2=40, 3=42, 4=?, 5=46 → from 42 to 46 is +4 over 2 steps → so +2 per step.
Try: Even numbers? Or just +2 each time.
Assume start before 40: 40 - 2 = 38 → first blank is 38
Sequence: 38, 40, 42, 44, 46, 48, 50, 52
Check positions:
1=?, 2=40, 3=42, 4=?, 5=46, 6=?, 7=50, 8=?
Yes: 38, 40, 42, 44, 46, 48, 50, 52
Missing: 38, 44, 48, 52
✔ Problem 8: 38, 40, 42, 44, 46, 48, 50, 52
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Final Answer:
1. 2, 3, 6, 7
2. 35, 36, 39, 41
3. 2, 8, 12, 16
4. 15, 20, 30, 40
5. 20, 22, 28, 32
6. 57, 59, 60, 61
7. 65, 70, 80, 95
8. 38, 44, 48, 52
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Problem 1: 1, __, __, 4, 5, __, __, 8
Look at the known numbers:
After 1 comes 4 → that’s +3 over two steps? Wait — let’s check from 4 to 5: that’s +1. Then 5 to 8 is +3 over two steps? Hmm.
Actually, let’s list positions:
Position: 1 2 3 4 5 6 7 8
Numbers: 1 ? ? 4 5 ? ? 8
From position 4 (number 4) to position 5 (number 5): +1
From position 5 (5) to position 8 (8): that’s 3 steps later → 5 to 8 is +3 → so maybe +1 per step?
Check: If we go +1 each time:
1, 2, 3, 4, 5, 6, 7, 8 → YES! That fits perfectly.
So missing numbers: 2, 3, 6, 7
✔ Problem 1: 1, 2, 3, 4, 5, 6, 7, 8
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Problem 2: 34, __, __, 37, 38, __, 40, __
Known: 34, then later 37, 38, 40
From 34 to 37: that’s +3 over 3 steps? Let’s count positions:
Pos: 1=34, 2=?, 3=?, 4=37, 5=38, 6=?, 7=40, 8=?
From pos 4 (37) to pos 5 (38): +1
From pos 5 (38) to pos 7 (40): that’s 2 steps → +2 → so likely +1 per step.
Try counting up by 1:
34, 35, 36, 37, 38, 39, 40, 41 → perfect!
Missing: 35, 36, 39, 41
✔ Problem 2: 34, 35, 36, 37, 38, 39, 40, 41
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Problem 3: __, 4, 6, __, 10, __, 14, __
Given: 4, 6, 10, 14
Look at differences:
6 - 4 = 2
10 - 6 = 4 → not consistent? Wait — maybe it’s increasing by 2 each time?
Wait: 4, 6 → +2
Then next should be 8? But it says blank, then 10 → yes! So if we assume +2 each time:
Start before 4: 4 - 2 = 2 → first blank is 2
Then: 4, 6, 8, 10, 12, 14, 16
Check positions:
Pos: 1=?, 2=4, 3=6, 4=?, 5=10, 6=?, 7=14, 8=?
If sequence is even numbers starting at 2:
2, 4, 6, 8, 10, 12, 14, 16 → matches all given!
Missing: 2, 8, 12, 16
✔ Problem 3: 2, 4, 6, 8, 10, 12, 14, 16
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Problem 4: 5, 10, __, __, 25, __, 35, __
Given: 5, 10, ..., 25, ..., 35, ...
Looks like multiples of 5?
5, 10, 15, 20, 25, 30, 35, 40 → yes!
Check:
Pos: 1=5, 2=10, 3=?, 4=?, 5=25, 6=?, 7=35, 8=?
So: 5, 10, 15, 20, 25, 30, 35, 40
Missing: 15, 20, 30, 40
✔ Problem 4: 5, 10, 15, 20, 25, 30, 35, 40
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Problem 5: 18, __, __, 24, 26, __, 30, __
Given: 18, ..., 24, 26, ..., 30, ...
Look at 24 to 26: +2
26 to 30: that’s +4 over 2 steps? Maybe +2 each time?
Try: Start at 18, add 2 each time:
18, 20, 22, 24, 26, 28, 30, 32 → perfect!
Positions:
1=18, 2=?, 3=?, 4=24, 5=26, 6=?, 7=30, 8=?
So: 18, 20, 22, 24, 26, 28, 30, 32
Missing: 20, 22, 28, 32
✔ Problem 5: 18, 20, 22, 24, 26, 28, 30, 32
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Problem 6: 56, __, 58, __, __, __, 62, 63
Given: 56, ?, 58, ?, ?, ?, 62, 63
Notice last two: 62, 63 → +1
Before that: 58 to 62 is 4 steps? Let’s map positions:
Pos: 1=56, 2=?, 3=58, 4=?, 5=?, 6=?, 7=62, 8=63
From pos 7 to 8: +1 → so probably counting up by 1.
Try full sequence: 56, 57, 58, 59, 60, 61, 62, 63 → yes!
Missing: 57, 59, 60, 61
✔ Problem 6: 56, 57, 58, 59, 60, 61, 62, 63
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Problem 7: 60, __, __, 75, __, 85, 90, __
Given: 60, ..., 75, ..., 85, 90, ...
Look at 85 to 90: +5
75 to 85: that’s 2 steps? From pos 4=75 to pos 6=85 → 2 steps → +10 → so +5 per step?
Try: Count by 5s starting at 60:
60, 65, 70, 75, 80, 85, 90, 95 → perfect!
Positions:
1=60, 2=?, 3=?, 4=75, 5=?, 6=85, 7=90, 8=?
So: 60, 65, 70, 75, 80, 85, 90, 95
Missing: 65, 70, 80, 95
✔ Problem 7: 60, 65, 70, 75, 80, 85, 90, 95
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Problem 8: __, 40, 42, __, 46, __, 50, __
Given: 40, 42, ..., 46, ..., 50, ...
40 to 42: +2
42 to 46: that’s 2 steps? Pos 2=40, 3=42, 4=?, 5=46 → from 42 to 46 is +4 over 2 steps → so +2 per step.
Try: Even numbers? Or just +2 each time.
Assume start before 40: 40 - 2 = 38 → first blank is 38
Sequence: 38, 40, 42, 44, 46, 48, 50, 52
Check positions:
1=?, 2=40, 3=42, 4=?, 5=46, 6=?, 7=50, 8=?
Yes: 38, 40, 42, 44, 46, 48, 50, 52
Missing: 38, 44, 48, 52
✔ Problem 8: 38, 40, 42, 44, 46, 48, 50, 52
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Final Answer:
1. 2, 3, 6, 7
2. 35, 36, 39, 41
3. 2, 8, 12, 16
4. 15, 20, 30, 40
5. 20, 22, 28, 32
6. 57, 59, 60, 61
7. 65, 70, 80, 95
8. 38, 44, 48, 52
Parent Tip: Review the logic above to help your child master the concept of number patterns worksheets.
