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 number, multiplying/dividing, or alternating operations).
2. Extend the sequence by finding the next two numbers.
3. State the rule.

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1) 56, 52, 48, 44, 40, 36, 32

- Differences:
52 - 56 = -4
48 - 52 = -4
44 - 48 = -4
So, it's decreasing by 4.

- Next two numbers:
32 - 4 = 28, then 28 - 4 = 24

✔ Pattern Rule: Subtract 4 each time.
✔ Next two numbers: 28, 24

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2) 22, 31, 40, 49, 58, 67, 76

- Differences:
31 - 22 = +9
40 - 31 = +9
49 - 40 = +9
So, increasing by 9.

- Next two numbers:
76 + 9 = 85, then 85 + 9 = 94

✔ Pattern Rule: Add 9 each time.
✔ Next two numbers: 85, 94

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3) 20, 25, 30, 35, 40, 45, 50

- Differences:
25 - 20 = +5
30 - 25 = +5
So, increasing by 5.

- Next two numbers:
50 + 5 = 55, then 55 + 5 = 60

✔ Pattern Rule: Add 5 each time.
✔ Next two numbers: 55, 60

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4) 73, 68, 63, 58, 53, 48, 43

- Differences:
68 - 73 = -5
63 - 68 = -5
So, decreasing by 5.

- Next two numbers:
43 - 5 = 38, then 38 - 5 = 33

✔ Pattern Rule: Subtract 5 each time.
✔ Next two numbers: 38, 33

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5) 75, 67, 59, 51, 43, 35, 27

- Differences:
67 - 75 = -8
59 - 67 = -8
So, decreasing by 8.

- Next two numbers:
27 - 8 = 19, then 19 - 8 = 11

✔ Pattern Rule: Subtract 8 each time.
✔ Next two numbers: 19, 11

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6) 85, 79, 73, 67, 61, 55, 49

- Differences:
79 - 85 = -6
73 - 79 = -6
So, decreasing by 6.

- Next two numbers:
49 - 6 = 43, then 43 - 6 = 37

✔ Pattern Rule: Subtract 6 each time.
✔ Next two numbers: 43, 37

---

7) 81, 79, 77, 75, 73, 69

Wait — let’s check the differences:
- 79 - 81 = -2
- 77 - 79 = -2
- 75 - 77 = -2
- 73 - 75 = -2
- But 69 - 73 = -4 → Not consistent!

Hmm — maybe typo? Let's look again.

Sequence: 81, 79, 77, 75, 73, 69

After 73, it drops to 69 — that's -4 instead of -2.

But if the pattern was subtracting 2, it should be:
81, 79, 77, 75, 73, 71, 69

Wait — but here it goes 73 → 69, so maybe it's still subtracting 2?

No: 73 → 69 is -4.

Alternatively, could it be an error in the sequence?

But let’s assume the pattern is subtract 2, and perhaps the last number is a typo?

But no — let’s double-check:
If it were subtracting 2:
81, 79, 77, 75, 73, 71, 69

So the sequence is correct:
81 → 79 (-2), 79 → 77 (-2), ..., 73 → 69 (-4)? No, that skips.

Wait — 73 → 69 is not -2. So unless there’s a mistake, maybe the pattern changes?

Wait — let’s recheck:
Is it possible that the sequence is:
81, 79, 77, 75, 73, 71, 69?

But the given sequence says: 81, 79, 77, 75, 73, 69

So after 73, it jumps to 69 — skipping 71.

That would break the pattern.

Wait — maybe it’s not subtracting 2 consistently?

But all previous steps are -2.

Unless the last one is wrong.

But assuming the pattern is subtract 2, then:

From 73:
73 - 2 = 71, then 71 - 2 = 69

So the sequence should be:
81, 79, 77, 75, 73, 71, 69

But the given list shows: 81, 79, 77, 75, 73, 69 — missing 71.

Wait — perhaps the number 71 is missing, and 69 is the sixth term?

Wait — count:

1. 81
2. 79
3. 77
4. 75
5. 73
6. 69 ← this is wrong if pattern is -2

So likely, the sequence is meant to be:
81, 79, 77, 75, 73, 71, 69

So either the printed sequence has a typo, or we’re missing something.

But the problem says: "Extend the next two numbers"

Given: 81, 79, 77, 75, 73, 69

Wait — from 73 to 69 is -4, not -2.

But before that, it was -2.

So maybe it’s alternating? Unlikely.

Or perhaps it's subtracting 2, and 69 is incorrect?

But let’s suppose the sequence is correct as written.

Then:
81 → 79 (-2)
79 → 77 (-2)
77 → 75 (-2)
75 → 73 (-2)
73 → 69 (-4)

That breaks the pattern.

Alternatively, maybe it's subtracting 2, and 69 is a typo for 71?

But since we have to work with what's given, perhaps it's subtracting 2, and the last number is just off?

Wait — maybe the pattern is subtract 2, and the sequence is:
81, 79, 77, 75, 73, 71, 69

So if the last number is 69, then the previous one must be 71.

But in the list, it says: 81, 79, 77, 75, 73, 69 — so 71 is missing.

So probably, the sequence is supposed to be:
81, 79, 77, 75, 73, 71, 69

Therefore, the pattern is subtract 2.

So even though 69 is listed, it's likely a typo or misprint.

But let's proceed assuming the pattern is subtract 2, and the last number is 69, which would mean the one before is 71 — but it's not listed.

Wait — the list is:
"7) 81, 79, 77, 75, 73, 69"

So six numbers: 81, 79, 77, 75, 73, 69

But 73 to 69 is -4, not -2.

So maybe the pattern changed?

But that seems unlikely.

Alternatively, could it be that the sequence is decreasing by 2, and 69 is a typo?

Yes — likely.

But since we must go by what's written, let's see if another pattern fits.

Try differences:

81 → 79: -2
79 → 77: -2
77 → 75: -2
75 → 73: -2
73 → 69: -4

No consistent pattern.

Wait — maybe it's subtracting 2, and the last number is 71, not 69?

But it says 69.

Perhaps the pattern is subtract 2, and the sequence is:
81, 79, 77, 75, 73, 71, 69

So if 69 is the sixth number, then 71 is fifth — but 73 is fifth.

So positions:

1. 81
2. 79
3. 77
4. 75
5. 73
6. 69

So 73 → 69 is -4 — doesn't fit.

Wait — maybe it's subtract 2, and the sequence is correct up to 73, then it continues: 71, 69.

But the list says 69 is the sixth number — so it's already given.

So the sequence is: 81, 79, 77, 75, 73, 69

So the next two numbers after 69?

If pattern is subtract 2, then after 69: 67, 65

But wait — how did it get from 73 to 69? That's -4.

So maybe it's not consistent.

Alternatively, perhaps the pattern is subtract 2, and the number 69 is a typo — it should be 71.

But since we can’t change it, maybe the pattern is:

Look at the numbers:
81, 79, 77, 75, 73, 69

From 73 to 69: -4

Maybe it’s subtract 2, then subtract 4, but that’s arbitrary.

Alternatively, perhaps the pattern is odd numbers decreasing by 2, but 69 is odd, yes.

But why skip 71?

Unless it’s not a typo.

Wait — perhaps the pattern is subtract 2, and the last number is 69, meaning the sequence is:

81, 79, 77, 75, 73, 71, 69

But the list only shows 6 numbers: 81, 79, 77, 75, 73, 69 — so 69 is the sixth number, implying 71 is missing.

So likely, the sequence is intended to be:
81, 79, 77, 75, 73, 71, 69

So the pattern is subtract 2.

Thus, even though 71 is missing in the list, we assume the pattern is subtract 2.

So the next two numbers after 69 would be:
69 - 2 = 67, then 65

✔ Pattern Rule: Subtract 2 each time.
✔ Next two numbers: 67, 65

(We’ll assume the sequence is meant to be decreasing by 2.)

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8) 90, 84, 78, 72, 66, 60, 54

- Differences:
84 - 90 = -6
78 - 84 = -6
So, decreasing by 6.

- Next two numbers:
54 - 6 = 48, then 48 - 6 = 42

✔ Pattern Rule: Subtract 6 each time.
✔ Next two numbers: 48, 42

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9) 60, 55, 50, 45, 40, 35, 30

- Differences:
55 - 60 = -5
50 - 55 = -5
So, decreasing by 5.

- Next two numbers:
30 - 5 = 25, then 25 - 5 = 20

✔ Pattern Rule: Subtract 5 each time.
✔ Next two numbers: 25, 20

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10) 81, 73, 65, 57, 49, 41, 33

- Differences:
73 - 81 = -8
65 - 73 = -8
So, decreasing by 8.

- Next two numbers:
33 - 8 = 25, then 25 - 8 = 17

✔ Pattern Rule: Subtract 8 each time.
✔ Next two numbers: 25, 17

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## ✔ Final Answers:

| # | Sequence | Next Two Numbers | Pattern Rule |
|---|--------|------------------|--------------|
| 1 | 56, 52, 48, 44, 40, 36, 32 | 28, 24 | Subtract 4 |
| 2 | 22, 31, 40, 49, 58, 67, 76 | 85, 94 | Add 9 |
| 3 | 20, 25, 30, 35, 40, 45, 50 | 55, 60 | Add 5 |
| 4 | 73, 68, 63, 58, 53, 48, 43 | 38, 33 | Subtract 5 |
| 5 | 75, 67, 59, 51, 43, 35, 27 | 19, 11 | Subtract 8 |
| 6 | 85, 79, 73, 67, 61, 55, 49 | 43, 37 | Subtract 6 |
| 7 | 81, 79, 77, 75, 73, 69 | 67, 65 | Subtract 2 *(assuming typo in sequence)* |
| 8 | 90, 84, 78, 72, 66, 60, 54 | 48, 42 | Subtract 6 |
| 9 | 60, 55, 50, 45, 40, 35, 30 | 25, 20 | Subtract 5 |
|10 | 81, 73, 65, 57, 49, 41, 33 | 25, 17 | Subtract 8 |

> 🟩 Note: For #7, the jump from 73 to 69 is -4 instead of -2, which breaks the pattern. It's likely a typo, and the intended sequence is decreasing by 2. Assuming that, the next numbers after 69 are 67 and 65.

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