Number Pattern Worksheets - Free Printable

Let’s solve each number pattern step by step. We’ll look at how the numbers change from one to the next — that’s called the “rule” of the pattern.

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Part A: Complete each number pattern

1) 6, 12, 18, 24, 30, ___, ___, ___
Look at the difference between numbers:
12 - 6 = 6
18 - 12 = 6
24 - 18 = 6
30 - 24 = 6
→ Rule: Add 6 each time.
Next: 30 + 6 = 36
Then: 36 + 6 = 42
Then: 42 + 6 = 48
✔ Answer: 36, 42, 48

2) 27, 42, 57, 72, 87, ___, ___, ___
Differences:
42 - 27 = 15
57 - 42 = 15
72 - 57 = 15
87 - 72 = 15
→ Rule: Add 15 each time.
Next: 87 + 15 = 102
Then: 102 + 15 = 117
Then: 117 + 15 = 132
✔ Answer: 102, 117, 132

3) 8, 16, 24, 32, 40, ___, ___, ___
Differences:
16 - 8 = 8
24 - 16 = 8
32 - 24 = 8
40 - 32 = 8
→ Rule: Add 8 each time.
Next: 40 + 8 = 48
Then: 48 + 8 = 56
Then: 56 + 8 = 64
✔ Answer: 48, 56, 64

4) 72, 66, 60, 54, 48, ___, ___, ___
Differences:
66 - 72 = -6 (or subtract 6)
60 - 66 = -6
54 - 60 = -6
48 - 54 = -6
→ Rule: Subtract 6 each time.
Next: 48 - 6 = 42
Then: 42 - 6 = 36
Then: 36 - 6 = 30
✔ Answer: 42, 36, 30

5) 5, 5, 5, 5, 5, 11, ___, ___, ___
First four are all 5s… then suddenly 11? That seems odd. Let’s check again.
Wait — maybe it’s a typo or trick? But looking closely:
It says: 5, 5, 5, 5, 5, 11 → that doesn’t follow an obvious math rule.
But perhaps it’s meant to be: 5, 11, 17, 23...? No, first five are 5s.
Alternatively — maybe it’s two patterns? Or maybe it’s a mistake?
Actually, let’s re-read: “5, 5, 5, 5, 5, 11” — that breaks the pattern.
Wait — perhaps it’s supposed to be: 5, 11, 17, 23... but written wrong?
No — let’s assume it’s correct as written. Maybe after five 5s, it starts adding 6?
5, 5, 5, 5, 5, 11 → 11 - 5 = 6
If we continue adding 6:
11 + 6 = 17
17 + 6 = 23
23 + 6 = 29
That could work — maybe the first five 5s are just setting up, and then it changes?
But that’s unusual. Alternatively, maybe it’s a misprint and should be 5, 11, 17...
Given the context of other problems, likely it’s meant to be increasing by 6 starting from 5.
But since first five are 5, perhaps it’s: repeat 5 five times, then add 6 each time?
So: 5, 5, 5, 5, 5, 11, 17, 23, 29
Yes — that makes sense if the pattern changes after position 5.
We’ll go with that.
✔ Answer: 17, 23, 29

*(Note: This one is tricky — if your teacher meant something else, double-check. But based on what’s written, this is logical.)*

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Part B: Identify each number pattern and fill in missing numbers

1) 88, ___, 90, ___, 94, ___, 98, ___, 100, ___, 104
Look at known numbers: 88, 90, 94, 98, 100, 104
From 88 to 90 → +2
90 to ? to 94 → probably +2 each time
Check: 88, 90, 92, 94, 96, 98, 100, 102, 104
Yes! So missing:
After 88 → 90 (given), so before 90 is already filled? Wait, blanks are:
Position: 88, [blank], 90, [blank], 94, [blank], 98, [blank], 100, [blank], 104
So:
Blank 1: between 88 and 90 → must be 89? But 88 to 90 is +2, so no integer in between unless it’s not consecutive.
Wait — 88, ?, 90 → if pattern is +1, then 89. But then 90 to ? to 94 → if +2, then 92. Inconsistent.
Better: Look at full sequence:
88, _, 90, _, 94, _, 98, _, 100, _, 104
Assume constant difference. From 88 to 90 is +2 over 2 steps → so +1 per step?
Try: 88, 89, 90, 91, 92, 93, 94... but then 94 to 98 is +4 over 2 steps → +2 per step? Not consistent.
Alternative: Maybe it’s even numbers? 88, 90, 92, 94, 96, 98, 100, 102, 104
But there are blanks between them. Count positions:
Total items: 11 numbers given with blanks.
List indices:
1: 88
2: ?
3: 90
4: ?
5: 94
6: ?
7: 98
8: ?
9: 100
10: ?
11: 104

From 1 to 3: 88 to 90 → +2 in 2 steps → +1 per step? Then pos2 = 89
Pos3 to pos5: 90 to 94 → +4 in 2 steps → +2 per step? Then pos4 = 92
Inconsistent.
Wait — perhaps it’s alternating? Or maybe I miscounted.
Another idea: Maybe the pattern is +2 every other number?
Look at odd positions: 1:88, 3:90, 5:94, 7:98, 9:100, 11:104
88 to 90: +2
90 to 94: +4
94 to 98: +4
98 to 100: +2
100 to 104: +4 — not consistent.
Perhaps it’s simply counting by 2s, and the blanks are where numbers are missing.
Standard even numbers: 88, 90, 92, 94, 96, 98, 100, 102, 104
But here we have 11 slots. Let’s map:
Slot 1: 88
Slot 2: should be 90? But slot 3 is 90 — conflict.
Unless the pattern is: start at 88, then add 1, then add 1, etc.?
Try filling sequentially:
Start at 88.
Next number: if +1 → 89
Then +1 → 90 (matches slot 3)
Then +2 → 92? But slot 5 is 94 — too big.
From slot 3 (90) to slot 5 (94): difference of 4 over 2 steps → +2 per step. So slot 4 = 92
Then slot 5: 94
Slot 6: ? to slot 7: 98 → difference 4 over 2 steps → +2 per step → slot 6 = 96
Slot 7: 98
Slot 8: ? to slot 9: 100 → difference 2 over 2 steps → +1 per step? Slot 8 = 99
But 98 to 99 to 100 — ok, but then slot 9: 100
Slot 10: ? to slot 11: 104 → difference 4 over 2 steps → +2 per step → slot 10 = 102
Now list:
1:88, 2:89, 3:90, 4:92, 5:94, 6:96, 7:98, 8:99, 9:100, 10:102, 11:104
Check differences:
88→89:+1, 89→90:+1, 90→92:+2, 92→94:+2, 94→96:+2, 96→98:+2, 98→99:+1, 99→100:+1, 100→102:+2, 102→104:+2
Not a single rule — messy.
Perhaps it's a typo, and it's meant to be consecutive even numbers with some missing.
Most logical: assume it's increasing by 2 each time, and the blanks are for the missing evens.
So: 88, 90, 92, 94, 96, 98, 100, 102, 104
But there are 11 positions. Perhaps the first blank is after 88, so:
88, [89?], 90, [91?], 94 — no.
Another approach: calculate the average increase.
From 88 to 104 is 16, over 10 intervals (since 11 numbers), so average +1.6 per step — not integer.
Perhaps it's two interleaved sequences?
Odd positions: 1:88, 3:90, 5:94, 7:98, 9:100, 11:104
Even positions: 2:?, 4:?, 6:?, 8:?, 10:?
For odd positions: 88,90,94,98,100,104
Differences: +2, +4, +4, +2, +4 — not clear.
Notice that 88,90,94,98,100,104 — these are all even, and close to multiples of 2.
Perhaps it's simply: the pattern is +2, but some numbers are skipped in the listing.
Let's count the gaps:
Between 88 and 90: one blank — so if +2 total, then each step +1, so blank = 89
Between 90 and 94: one blank — +4 total, so each step +2, blank = 92
Between 94 and 98: one blank — +4 total, blank = 96
Between 98 and 100: one blank — +2 total, blank = 99
Between 100 and 104: one blank — +4 total, blank = 102
So the sequence is: 88, 89, 90, 92, 94, 96, 98, 99, 100, 102, 104
And the rule is not constant, but the missing numbers are 89, 92, 96, 99, 102
But the problem says "identify the number pattern" — implying a single rule.
Perhaps it's a mistake, and it should be 88, 90, 92, 94, 96, 98, 100, 102, 104 with no extra blanks.
Given that, and to keep it simple, I think the intended pattern is adding 2 each time, and the blanks are for the intermediate even numbers.
So for: 88, ___, 90, ___, 94, ___, 98, ___, 100, ___, 104
If we assume it's 88, 90, 92, 94, 96, 98, 100, 102, 104, then the blanks are at positions 2,4,6,8,10 which should be 90,92,96,100,102 — but 90 is already at position 3, so conflict.
Unless the first blank is 89, but that's odd.
Let's look at the numbers given: 88, then blank, then 90 — so likely the blank is 89 if counting by 1s.
Then 90 to blank to 94 — if counting by 2s, blank is 92.
Then 94 to blank to 98 — blank is 96.
Then 98 to blank to 100 — blank is 99.
Then 100 to blank to 104 — blank is 102.
So the missing numbers are: 89, 92, 96, 99, 102
And the pattern is not uniform, but that's what fits.
Perhaps the pattern is: add 1, add 1, add 2, add 2, add 2, add 2, add 1, add 1, add 2, add 2 — but that's complicated.
For a student, likely they expect: the numbers are increasing, and you fill in the obvious missing integers.
So I'll go with:
88, 89, 90, 92, 94, 96, 98, 99, 100, 102, 104
Missing: 89, 92, 96, 99, 102
But let's verify with the last part: 100 to 104 with one blank — 102 makes sense.
Okay, we'll use that.
✔ Answer: 89, 92, 96, 99, 102

2) 2, ___, 4, ___, 6, ___, 8, ___, 10, ___, 12
This looks like counting by 2s, but with blanks between.
Positions: 1:2, 2:?, 3:4, 4:?, 5:6, 6:?, 7:8, 8:?, 9:10, 10:?, 11:12
From 2 to 4: +2 over 2 steps → +1 per step, so blank2 = 3
4 to 6: +2 over 2 steps → blank4 = 5
6 to 8: +2 over 2 steps → blank6 = 7
8 to 10: +2 over 2 steps → blank8 = 9
10 to 12: +2 over 2 steps → blank10 = 11
So sequence: 2,3,4,5,6,7,8,9,10,11,12
Rule: add 1 each time.
✔ Answer: 3, 5, 7, 9, 11

3) 12, ___, 22, ___, 32, ___, 42, ___, 52, ___, 62
Similar structure.
Positions: 1:12, 2:?, 3:22, 4:?, 5:32, 6:?, 7:42, 8:?, 9:52, 10:?, 11:62
From 12 to 22: +10 over 2 steps → +5 per step, so blank2 = 17
22 to 32: +10 over 2 steps → blank4 = 27
32 to 42: +10 over 2 steps → blank6 = 37
42 to 52: +10 over 2 steps → blank8 = 47
52 to 62: +10 over 2 steps → blank10 = 57
Sequence: 12,17,22,27,32,37,42,47,52,57,62
Rule: add 5 each time.
✔ Answer: 17, 27, 37, 47, 57

4) 28, ___, 32, ___, 36, ___, 40, ___, 44, ___, 48
Positions: 1:28, 2:?, 3:32, 4:?, 5:36, 6:?, 7:40, 8:?, 9:44, 10:?, 11:48
28 to 32: +4 over 2 steps → +2 per step, blank2 = 30
32 to 36: +4 over 2 steps → blank4 = 34
36 to 40: +4 over 2 steps → blank6 = 38
40 to 44: +4 over 2 steps → blank8 = 42
44 to 48: +4 over 2 steps → blank10 = 46
Sequence: 28,30,32,34,36,38,40,42,44,46,48
Rule: add 2 each time.
✔ Answer: 30, 34, 38, 42, 46

5) 84, ___, 78, ___, 72, ___, 66, ___, 60, ___, 54
Decreasing.
Positions: 1:84, 2:?, 3:78, 4:?, 5:72, 6:?, 7:66, 8:?, 9:60, 10:?, 11:54
84 to 78: -6 over 2 steps → -3 per step, blank2 = 81
78 to 72: -6 over 2 steps → blank4 = 75
72 to 66: -6 over 2 steps → blank6 = 69
66 to 60: -6 over 2 steps → blank8 = 63
60 to 54: -6 over 2 steps → blank10 = 57
Sequence: 84,81,78,75,72,69,66,63,60,57,54
Rule: subtract 3 each time.
✔ Answer: 81, 75, 69, 63, 57

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Final Answer:

Part A:
1) 36, 42, 48
2) 102, 117, 132
3) 48, 56, 64
4) 42, 36, 30
5) 17, 23, 29

Part B:
1) 89, 92, 96, 99, 102
2) 3, 5, 7, 9, 11
3) 17, 27, 37, 47, 57
4) 30, 34, 38, 42, 46
5) 81, 75, 69, 63, 57