Number Patterns Worksheets - Free Printable

Let's solve each number pattern step by step. For each sequence, we'll:

1. Identify the pattern (e.g., adding/subtracting a constant, alternating operations, etc.).
2. Extend the sequence by finding the next two numbers.
3. State the rule clearly.

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1) 21, 27, 33, 39, 45, 51, 57

- Differences:
27 - 21 = 6
33 - 27 = 6
39 - 33 = 6
→ Pattern: +6 each time
- Next two numbers:
57 + 6 = 63
63 + 6 = 69
- Rule: Add 6

✔ Answer: 63, 69 — Add 6

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2) 69, 64, 59, 54, 49, 44, 39

- Differences:
64 - 69 = -5
59 - 64 = -5
54 - 59 = -5
→ Pattern: -5 each time
- Next two numbers:
39 - 5 = 34
34 - 5 = 29
- Rule: Subtract 5

✔ Answer: 34, 29 — Subtract 5

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3) 79, 70, 61, 52, 43, 34, 25

- Differences:
70 - 79 = -9
61 - 70 = -9
52 - 61 = -9
→ Pattern: -9 each time
- Next two numbers:
25 - 9 = 16
16 - 9 = 7
- Rule: Subtract 9

✔ Answer: 16, 7 — Subtract 9

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4) 83, 74, 65, 56, 47, 38, 29

- Differences:
74 - 83 = -9
65 - 74 = -9
56 - 65 = -9
→ Pattern: -9 each time
- Next two numbers:
29 - 9 = 20
20 - 9 = 11
- Rule: Subtract 9

✔ Answer: 20, 11 — Subtract 9

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5) 77, 70, 63, 56, 49, 42, 35

- Differences:
70 - 77 = -7
63 - 70 = -7
56 - 63 = -7
→ Pattern: -7 each time
- Next two numbers:
35 - 7 = 28
28 - 7 = 21
- Rule: Subtract 7

✔ Answer: 28, 21 — Subtract 7

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6) 30, 35, 40, 45, 50, 55, 60

- Differences:
35 - 30 = +5
40 - 35 = +5
45 - 40 = +5
→ Pattern: +5 each time
- Next two numbers:
60 + 5 = 65
65 + 5 = 70
- Rule: Add 5

✔ Answer: 65, 70 — Add 5

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7) 44, 46, 48, 50, 52, 54

- Differences:
46 - 44 = +2
48 - 46 = +2
50 - 48 = +2
→ Pattern: +2 each time
- Next two numbers:
54 + 2 = 56
56 + 2 = 58
- Rule: Add 2

✔ Answer: 56, 58 — Add 2

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8) 85, 78, 71, 64, 57, 50, 43

- Differences:
78 - 85 = -7
71 - 78 = -7
64 - 71 = -7
→ Pattern: -7 each time
- Next two numbers:
43 - 7 = 36
36 - 7 = 29
- Rule: Subtract 7

✔ Answer: 36, 29 — Subtract 7

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9) 20, 26, 32, 38, 44, 50, 56

- Differences:
26 - 20 = +6
32 - 26 = +6
38 - 32 = +6
→ Pattern: +6 each time
- Next two numbers:
56 + 6 = 62
62 + 6 = 68
- Rule: Add 6

✔ Answer: 62, 68 — Add 6

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10) 64, 61, 58, 55, 49, 46

Wait! Let's check this one carefully.

Sequence: 64, 61, 58, 55, 49, 46

Differences:
- 61 - 64 = -3
- 58 - 61 = -3
- 55 - 58 = -3
- 49 - 55 = -6 ← Not consistent!
- 46 - 49 = -3

Hmm, that’s odd. From 55 to 49 is -6, but others are -3.

Let’s look again:
- 64 → 61 → -3
- 61 → 58 → -3
- 58 → 55 → -3
- 55 → 49 → -6
- 49 → 46 → -3

So maybe a typo? Or perhaps it's not arithmetic?

Wait — could it be alternating patterns?

But let's double-check the numbers.

Wait — maybe there’s a mistake in the sequence?

Wait: After 55, if it were 52, then 52 → 49 → -3, and 49 → 46 → -3.

But here it's 49, so from 55 → 49 = -6.

That breaks the pattern.

But looking at the sequence again:

64, 61, 58, 55, 49, 46

Let’s list positions:

1. 64
2. 61 (-3)
3. 58 (-3)
4. 55 (-3)
5. 49 (-6) ← big jump
6. 46 (-3)

Possibly a typo? Maybe it should be 52 instead of 49?

But assuming the sequence is correct as given, let's see:

From 55 to 49: -6
Then 49 to 46: -3

Maybe the pattern is -3, -3, -3, -6, -3? That doesn’t repeat.

Alternatively, maybe it's subtracting 3, then 3, then 3, then 6, then 3 — not helpful.

Wait — could it be that the sequence is decreasing by 3, but one number is off?

Let’s assume the intended pattern is subtract 3.

Then:
- 64 → 61 → 58 → 55 → 52 → 49 → 46

But here, it skips 52 and goes to 49.

But in the sequence, after 55 comes 49, which is -6.

Then 49 → 46 = -3.

So maybe the pattern is: subtract 3, subtract 3, subtract 3, subtract 6, subtract 3?

Not consistent.

Wait — what if the pattern is alternate subtraction?

No — all others are consistent.

Wait — maybe it's subtract 3, but one number is missing?

But no, there are 6 numbers listed.

Wait — let's try another idea.

What if it's subtract 3, but there’s a typo in the sequence?

For example, if it was supposed to be:

64, 61, 58, 55, 52, 49, 46 → then it would be -3 each time.

But it says 49, not 52.

But wait — the fifth number is 49, sixth is 46.

So 55 → 49 = -6
49 → 46 = -3

So maybe the pattern is: subtract 3, subtract 3, subtract 3, subtract 6, subtract 3...

Still inconsistent.

Wait — could it be subtract 3, but one value is wrong?

Alternatively, maybe the sequence is:

64, 61, 58, 55, 49, 46

Check differences:
64 → 61 = -3
61 → 58 = -3
58 → 55 = -3
55 → 49 = -6
49 → 46 = -3

So the pattern might be: -3, -3, -3, -6, -3 — no clear rule.

But wait — maybe it's subtract 3, but skip one?

Alternatively, maybe it's not arithmetic.

Wait — another idea: maybe the sequence has an error.

But let's suppose the pattern is meant to be subtract 3.

Then:
- After 55: 55 - 3 = 52
- Then 52 - 3 = 49
- Then 49 - 3 = 46

So the sequence should be:
64, 61, 58, 55, 52, 49, 46

But in the problem, it's written as:
64, 61, 58, 55, 49, 46

So 52 is missing, and 49 appears too early.

So likely, the fifth number is a typo — it should be 52, not 49.

But since the problem gives 49, we have to work with it.

So sequence: 64, 61, 58, 55, 49, 46

Now, from 55 to 49 = -6
Then 49 to 46 = -3

So perhaps the pattern is alternating between -3 and -6?

But earlier it was three -3s.

Let’s see:

1. 64
2. 61 (-3)
3. 58 (-3)
4. 55 (-3)
5. 49 (-6)
6. 46 (-3)

So maybe the pattern changes?

But that seems unlikely.

Wait — could it be subtract 3, but one number is incorrect?

Given that all other sequences follow a clear pattern, and this one has a break, it's possible the fifth number is meant to be 52, not 49.

But since it's written as 49, we’ll go with it.

So from 46, if we continue the -3 pattern (since last change was -3), then:

- 46 - 3 = 43
- 43 - 3 = 40

But that assumes the pattern resumes.

But before that, we had a -6.

So maybe the pattern is: subtract 3, subtract 3, subtract 3, subtract 6, subtract 3, subtract 3

But why?

Alternatively, maybe it's subtract 3, but the number 49 is a typo.

But let's suppose it's correct.

Wait — another idea: maybe it's subtract 3, and 49 is actually the result of 52 - 3, but 52 is skipped?

No.

Wait — perhaps the sequence is:

64, 61, 58, 55, 49, 46

Let’s look at the numbers:

64 → 61 → 58 → 55 → 49 → 46

Is there another way?

Wait — maybe it's subtract 3, but 49 is a typo for 52?

Yes, that makes sense.

Because 55 - 3 = 52, 52 - 3 = 49, 49 - 3 = 46.

So the sequence should be:
64, 61, 58, 55, 52, 49, 46

But in the problem, it's written as:
64, 61, 58, 55, 49, 46

So 52 is missing, and 49 appears twice?

No — 55 → 49 is a jump of -6.

So unless the pattern is -3, -3, -3, -6, -3, which is inconsistent.

But let's assume it's a typo and the fifth number is 52, not 49.

But since the problem says 49, we must use it.

So the sequence is:
64, 61, 58, 55, 49, 46

Now, from 55 to 49 = -6
From 49 to 46 = -3

So maybe the pattern is: -3, -3, -3, -6, -3

Then next: -3 → 46 - 3 = 43, then 40

But that’s arbitrary.

Alternatively, maybe the pattern is subtract 3, and the 49 is a typo, and it should be 52.

In that case, the sequence is:

64, 61, 58, 55, 52, 49, 46

Then next: 46 - 3 = 43, then 40

And the rule is subtract 3

But in the problem, it's written as: 64, 61, 58, 55, 49, 46 — skipping 52.

So either:

- It's a typo, or
- The pattern changes.

But given the context of the worksheet (all others are simple arithmetic), it's highly likely that 49 is a typo and should be 52.

But since we can't change the problem, let's assume the pattern is subtract 3, and the number 49 is incorrect.

But wait — maybe the sequence is 64, 61, 58, 55, 49, 46, and we accept that from 55 to 49 is -6, then -3.

But then the pattern isn't consistent.

Alternatively, maybe it's subtract 3, and the fifth number is 52, but printed as 49 by mistake.

Given that, and to match the expected format, I think the intended sequence is:

64, 61, 58, 55, 52, 49, 46 — but the problem lists 49 as the fifth number.

Wait — no: the sequence is:

"64, 61, 58, 55, 49, 46"

So:

1. 64
2. 61
3. 58
4. 55
5. 49
6. 46

So position 5 is 49.

So from 55 to 49 = -6
From 49 to 46 = -3

So perhaps the pattern is -3, -3, -3, -6, -3

Then next: -3 → 46 - 3 = 43, then 40

But that’s weak.

Alternatively, maybe it's subtract 3, and the 49 is a typo for 52, and the sequence is:

64, 61, 58, 55, 52, 49, 46 — but then 55 to 52 = -3, 52 to 49 = -3, 49 to 46 = -3

So pattern: subtract 3

Then next two: 46 - 3 = 43, 43 - 3 = 40

And the fifth number should be 52, not 49.

But in the problem, it's 49, so either it's a typo, or we accept the inconsistency.

Given that, and since the rest of the worksheet has clean patterns, I believe 49 is a typo and should be 52.

So the correct sequence is:
64, 61, 58, 55, 52, 49, 46

Pattern: Subtract 3

Next two: 46 - 3 = 43, 43 - 3 = 40

So even though the problem says "49", it's likely a typo.

Thus:

✔ Answer: 43, 40 — Subtract 3

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Final Answers:

1) 63, 69 — Add 6
2) 34, 29 — Subtract 5
3) 16, 7 — Subtract 9
4) 20, 11 — Subtract 9
5) 28, 21 — Subtract 7
6) 65, 70 — Add 5
7) 56, 58 — Add 2
8) 36, 29 — Subtract 7
9) 62, 68 — Add 6
10) 43, 40 — Subtract 3 *(assuming 49 is a typo; intended pattern is -3)*

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Note: For #10, the sequence as written (64, 61, 58, 55, 49, 46) has a break in the pattern (jump from 55 to 49 is -6). However, given the context and consistency with other problems, it's likely a typo, and the intended fifth number is 52, making the pattern consistently subtract 3. Thus, the next two numbers are 43 and 40.