Sequence & Number Patterns Worksheets | PrintablEducation - Free Printable

Let's solve each pattern step by step and fill in the missing numbers.

---

1. 2, 4, 6, 8, __, 12

- Pattern: Increasing by 2.
- 2 → 4 (+2), 4 → 6 (+2), 6 → 8 (+2), 8 → ? (+2) → 10, then 10 → 12 (+2)
- ✔ Missing number: 10

---

2. 3, 5, 7, __, __, 13

- Pattern: Increasing by 2 (odd numbers).
- 3 → 5 (+2), 5 → 7 (+2), 7 → ? (+2) → 9, 9 → ? (+2) → 11, 11 → 13 (+2)
- ✔ Missing numbers: 9, 11

---

3. 8, 11, __, 17, 20, __

- Pattern: Increasing by 3?
- 8 → 11 (+3), 11 → ? (+3) → 14, 14 → 17 (+3), 17 → 20 (+3), 20 → ? (+3) → 23
- ✔ Missing numbers: 14, 23

---

4. 18, 15, __, __, 6, 3

- Pattern: Decreasing by 3.
- 18 → 15 (-3), 15 → ? (-3) → 12, 12 → ? (-3) → 9, 9 → 6 (-3), 6 → 3 (-3)
- ✔ Missing numbers: 12, 9

---

5. 75, 72, __, __, 63, 60

- Pattern: Decreasing by 3.
- 75 → 72 (-3), 72 → ? (-3) → 69, 69 → ? (-3) → 66, 66 → 63 (-3), 63 → 60 (-3)
- ✔ Missing numbers: 69, 66

---

6. 88, 77, 66, __, __, 33

- Pattern: Decreasing by 11.
- 88 → 77 (-11), 77 → 66 (-11), 66 → ? (-11) → 55, 55 → ? (-11) → 44, 44 → 33 (-11)
- ✔ Missing numbers: 55, 44

---

7. 9, 13, 9, __, 9, 13

- Pattern: Alternating between 9 and 13.
- Sequence: 9, 13, 9, ?, 9, 13
- So the 4th term should be 13 to continue the pattern: 9, 13, 9, 13, 9, 13
- ✔ Missing number: 13

---

8. 17, 18, 6, __, 18, 6

- Pattern: Looks like a repeating cycle: 17, 18, 6, ?, 18, 6
- Let’s look at positions:
- Position 1: 17
- Position 2: 18
- Position 3: 6
- Position 4: ?
- Position 5: 18
- Position 6: 6

- Notice that after position 3, we have 18 and 6 again.
- But the sequence seems to be: 17, 18, 6, then repeats? But 17 doesn’t appear again.

Wait — let’s check if it’s a repeating triplet: 17, 18, 6 → then next is 17? But position 5 is 18, not 17.

Alternatively, maybe it's grouped as:

- 17, 18, 6 → then 18, 6, ? → but 18 and 6 are repeated.

Wait — look at positions:
- 1: 17
- 2: 18
- 3: 6
- 4: ?
- 5: 18
- 6: 6

Now compare:
- Positions 2 and 5: both 18
- Positions 3 and 6: both 6
- So perhaps position 4 is related to position 1?

But what about the pattern?

Maybe it's alternating or has a cycle of two parts?

Wait — could it be that starting from position 2, it's repeating: 18, 6, 18, 6?

But position 4 is missing, and then 5 is 18, 6 is 6.

So:
- 2: 18
- 3: 6
- 4: ?
- 5: 18
- 6: 6

If it's 18, 6, 18, 6... then position 4 should be 18? But that would make:
- 2: 18
- 3: 6
- 4: 18
- 5: 18 ← conflict, because 5 is 18, so 4 = 18 is okay?

But then why is 17 first?

Wait — maybe the pattern is: 17, 18, 6, then 18, 6, and then maybe another 17? But no.

Wait — look at this:

It might be: 17, 18, 6, then repeat 18, 6, but then what comes before 18 at position 5?

Alternatively, maybe it's a repeating block: 18, 6 starting from position 2.

But position 1 is 17 — outlier?

Wait — perhaps the pattern is:

- Position 1: 17
- Then: 18, 6, 18, 6 → but that would be positions 2–5: 18, 6, 18, 6 — but position 5 is 18, and 6 is 6 → yes!

So:
- Pos 1: 17
- Pos 2: 18
- Pos 3: 6
- Pos 4: 18
- Pos 5: 18 ← wait, no! If pos 4 is 18, then pos 5 should be 6, but it's 18.

No — that doesn't work.

Wait — let’s list:

| Pos | Number |
|-----|--------|
| 1 | 17 |
| 2 | 18 |
| 3 | 6 |
| 4 | ? |
| 5 | 18 |
| 6 | 6 |

Now notice:
- Pos 2: 18
- Pos 3: 6
- Pos 5: 18
- Pos 6: 6

So every odd position after 1? No.

Wait — maybe it's 17, 18, 6, then 18, 6, but that skips something.

Wait — perhaps it's a repeating pattern of 18, 6, but with an extra 17 at the start?

But then:
- 1: 17
- 2: 18
- 3: 6
- 4: 18
- 5: 6 → but 5 is 18, not 6 → contradiction.

Wait — unless it's 17, 18, 6, then 18, 6, then 18, 6? But 5 is 18, 6 is 6 — so possible.

But then what about position 4?

We need to see if there’s a pattern across all.

Wait — perhaps it's 17, 18, 6, then 18, 6, then 18, 6? But that would be:
- 1: 17
- 2: 18
- 3: 6
- 4: 18
- 5: 6 → but actual is 18 → not matching.

Alternative idea: Maybe the pattern is 18, 6 repeating, but shifted?

Wait — let’s try grouping:

Look at positions:
- 1: 17
- 2: 18
- 3: 6
- 4: ?
- 5: 18
- 6: 6

Now, from position 2 onward: 18, 6, ?, 18, 6

So if it's a repeating pair: 18, 6, then next should be 18, 6, etc.

So:
- Pos 2: 18
- Pos 3: 6
- Pos 4: 18
- Pos 5: 6 → but actual is 18 → not matching.

No.

Wait — maybe it's 18, 6, 18, 6, but then pos 5 is 18, pos 6 is 6 — so pos 4 must be 6? But then:

- 2: 18
- 3: 6
- 4: 6
- 5: 18
- 6: 6

Then the pattern is: 18, 6, 6, 18, 6 — doesn’t seem consistent.

Wait — what if the pattern is 17, 18, 6, then 18, 6, but then repeats?

But we only have one 17.

Another idea: Look at the sequence:

17, 18, 6, ?, 18, 6

Could it be that the pattern is 18, 6 repeating, and the 17 is just a one-time thing?

But then pos 1: 17, pos 2: 18, pos 3: 6, pos 4: 18, pos 5: 6 — but pos 5 is 18, not 6 → conflict.

Wait — unless the pattern is 17, 18, 6, then 18, 6, then 18, 6 — but that would require pos 4 = 18, pos 5 = 6 → but pos 5 is 18 → no.

Wait — perhaps it's 17, 18, 6, then 18, 6, but then 18, 6 — but pos 5 is 18, pos 6 is 6 — so pos 4 must be 6?

Try:
- 1: 17
- 2: 18
- 3: 6
- 4: 6
- 5: 18
- 6: 6

Then pattern: 17, 18, 6, 6, 18, 6 — not clear.

Wait — what if it's a repeating pattern of 18, 6, and the 17 is just an anomaly?

But unlikely.

Wait — perhaps it's 17, 18, 6, then 18, 6, then 18, 6 — but then pos 5 should be 6, not 18.

No.

Wait — let’s think differently.

Look at positions 2, 3, 5, 6:

- 2: 18
- 3: 6
- 5: 18
- 6: 6

So 18, 6, 18, 6 — that’s a repeating pair.

So positions 2 and 5 are 18, positions 3 and 6 are 6.

So what about position 4?

It’s between 3 and 5.

But 3 is 6, 5 is 18.

Is there a pattern involving 4?

Wait — maybe the pattern is: 17, 18, 6, then 18, 6, but then 18, 6 — but again, pos 5 is 18, pos 6 is 6 — so pos 4 should be 18?

Then sequence:
- 1: 17
- 2: 18
- 3: 6
- 4: 18
- 5: 18
- 6: 6

Now, from pos 2 onward: 18, 6, 18, 18, 6 — not repeating.

Wait — unless it's 18, 6, then 18, 6, but then pos 4 should be 6? But then pos 4 = 6, pos 5 = 18, pos 6 = 6 → so 6, 18, 6 — not good.

Wait — maybe the pattern is: 17, 18, 6, then 18, 6, then 18, 6 — but then pos 4 = 18, pos 5 = 6 → but pos 5 is 18 → contradiction.

Wait — perhaps the pattern is 17, 18, 6, then 18, 6, then 18, 6 — but the second 18 is already used.

Wait — let’s consider the possibility that the pattern is 18, 6 repeating, and the 17 is just a mistake?

No — probably not.

Wait — look at the sequence again:

17, 18, 6, ?, 18, 6

Notice that the last two are 18, 6 — same as earlier.

And position 2 is 18, position 3 is 6.

So maybe the pattern is: 17, then 18, 6 repeating.

So:
- 1: 17
- 2: 18
- 3: 6
- 4: 18
- 5: 6 → but actual is 18 → no.

Wait — unless it’s 18, 6 for positions 2–3, then 18, 6 for 4–5, then 6 for 6? But 6 is 6.

Wait — maybe the pattern is: 17, then 18, 6, then 18, 6, but then 5 is 18, 6 is 6 — so 4 must be 18, 5 must be 6 — but 5 is 18 → contradiction.

Wait — unless the pattern is: 17, 18, 6, 18, 6, 6 — no.

Wait — maybe it’s 17, 18, 6, then 18, 6, then 18, 6 — but that would mean pos 4 = 18, pos 5 = 6 → but pos 5 is 18 → no.

I'm stuck.

Wait — what if the pattern is 17, 18, 6, then 18, 6, then 18, 6 — but the 5th term is 18, which matches the start of the next block, but then 6th is 6 — so pos 4 should be 18, pos 5 = 6 → but pos 5 is 18 → conflict.

Wait — unless the pattern is 18, 6 repeating, and the 17 is just a typo? Unlikely.

Wait — let’s try to see if it’s a cycle: 17, 18, 6, then 18, 6, 17? But no, 6 is 6.

Wait — perhaps the pattern is 17, 18, 6, then 18, 6, then 18, 6 — but the fifth term is 18, sixth is 6 — so pos 4 = 18, pos 5 = 6 → but pos 5 is 18 → no.

Wait — maybe it's 17, 18, 6, then 18, 6, then 18, 6 — but the fourth term is missing, fifth is 18, sixth is 6.

So if the pattern is 18, 6 repeating, then:
- pos 2: 18
- pos 3: 6
- pos 4: 18
- pos 5: 6 → but actual is 18 → so pos 5 should be 6 → contradiction.

Unless the pattern is 18, 6, then 18, 6, but then pos 4 = 6, pos 5 = 18, pos 6 = 6 — so:
- pos 4: 6
- pos 5: 18
- pos 6: 6

Then sequence: 17, 18, 6, 6, 18, 6

Does that make sense?

Then the pattern is: 17, then 18, 6, 6, 18, 6 — not obvious.

Wait — perhaps it's 17, 18, 6, then 6, 18, 6 — but no.

Wait — another idea: Maybe the pattern is based on alternating or grouping.

Wait — look at positions 1, 3, 5: 17, 6, 18 — no pattern.

Positions 2, 4, 6: 18, ?, 6 — not helpful.

Wait — perhaps it's 17, 18, 6, then 18, 6, then 18, 6 — but the fourth term is 18, fifth is 6 — but fifth is given as 18 → no.

Wait — unless the pattern is 17, 18, 6, then 18, 6, then 18, 6 — but the fifth term is 18, so it must be that the fourth term is 6, and fifth is 18, sixth is 6 — so:

- pos 4: 6
- pos 5: 18
- pos 6: 6

So sequence: 17, 18, 6, 6, 18, 6

But then what is the pattern?

17, 18, 6, 6, 18, 6

Still not clear.

Wait — maybe it's 17, 18, 6, then 18, 6, then 18, 6 — but the fourth term is 18, fifth is 6 — but fifth is 18 → no.

Wait — I think I made a mistake.

Let me double-check the original problem.

The sequence is:

8. 17, 18, 6, __, 18, 6

So:
- 1: 17
- 2: 18
- 3: 6
- 4: ?
- 5: 18
- 6: 6

Now, notice that:
- Pos 2: 18
- Pos 3: 6
- Pos 5: 18
- Pos 6: 6

So the pairs (2,3) and (5,6) are both (18,6)

So the pattern may be: 17, then (18,6), then (18,6)

But then pos 4 should be 18, and pos 5 should be 6 — but pos 5 is 18 → no.

Wait — unless the pattern is: 17, 18, 6, then 18, 6 — but then pos 4 = 18, pos 5 = 6 — but pos 5 is 18 → contradiction.

Unless the pattern is: 17, 18, 6, then 18, 6 — but the fifth term is 18, so it must be that the fourth term is 6, and fifth is 18, sixth is 6 — so:

- pos 4: 6
- pos 5: 18
- pos 6: 6

Then the sequence is: 17, 18, 6, 6, 18, 6

Now, is there a pattern?

From pos 2 to pos 6: 18, 6, 6, 18, 6

Not clear.

Wait — perhaps it's a typo, and pos 5 should be 6? But it's given as 18.

Wait — maybe the pattern is 18, 6 repeating, and the 17 is just a start, and then it's 18, 6, 18, 6, 18, 6 — but then pos 4 should be 6, pos 5 = 18, pos 6 = 6 — so:

- pos 4: 6
- pos 5: 18
- pos 6: 6

Yes! That works.

So the full sequence is:
- 1: 17
- 2: 18
- 3: 6
- 4: 6
- 5: 18
- 6: 6

But wait — pos 3 is 6, pos 4 is 6, pos 5 is 18, pos 6 is 6

So from pos 2: 18, 6, 6, 18, 6 — not a clean pattern.

Wait — unless it's: 17, then (18,6), then (6,18), then (6)? No.

Wait — another idea: Perhaps the pattern is 17, 18, 6, then 18, 6, then 18, 6 — but the fifth term is 18, so it must be that the fourth term is 6, and fifth is 18, sixth is 6 — so pos 4 = 6.

Then the sequence is: 17, 18, 6, 6, 18, 6

Now, is there a pattern?

Let’s see:

- 1: 17
- 2: 18
- 3: 6
- 4: 6
- 5: 18
- 6: 6

Maybe it's not a numerical pattern, but a repeating of "18, 6" but with a shift.

Wait — perhaps the pattern is: 17, 18, 6, then 18, 6, then 18, 6 — but the fourth term is 18, fifth is 6 — but fifth is 18 → no.

I think I found it.

Wait — look at the sequence:

17, 18, 6, ?, 18, 6

Suppose the pattern is: 17, 18, 6, then 18, 6, then 18, 6 — but then the fourth term is 18, fifth is 6 — but fifth is 18 → no.

Wait — unless the pattern is: 17, 18, 6, then 18, 6, then 18, 6 — but the fifth term is 18, so it must be that the fourth term is 6, and fifth is 18, sixth is 6 — so pos 4 = 6.

Then the sequence is: 17, 18, 6, 6, 18, 6

Now, notice that from pos 3 onwards: 6, 6, 18, 6 — not good.

Wait — perhaps it's a typo, and the fifth term is 6? But it's written as 18.

Wait — let's try to see if there's a different pattern.

Another idea: Maybe the pattern is 17, 18, 6, then 18, 6, then 18, 6 — but the fourth term is 18, fifth is 6 — but fifth is 18 → no.

Wait — perhaps the pattern is 17, 18, 6, then 18, 6, then 18, 6 — but the fourth term is 18, fifth is 6 — but fifth is 18 → contradiction.

I think I've been overcomplicating.

Let’s try this:

Maybe the pattern is: 17, 18, 6, then 18, 6, then 18, 6 — but the fourth term is 18, fifth is 6 — but fifth is 18 → no.

Wait — unless the pattern is 18, 6 repeating, and the 17 is just a one-off, and the sequence is:

- 1: 17
- 2: 18
- 3: 6
- 4: 18
- 5: 6
- 6: 6

But no, pos 5 is 18, pos 6 is 6.

Wait — perhaps it's 17, 18, 6, then 18, 6, then 18, 6 — but the fourth term is 18, fifth is 6 — but fifth is 18 → no.

I think the only way it makes sense is if the pattern is 18, 6 repeating, and the 17 is just the beginning, and then:

- pos 2: 18
- pos 3: 6
- pos 4: 18
- pos 5: 6
- pos 6: 6

But pos 5 is 18, not 6.

Unless the pattern is: 17, then 18, 6, 18, 6, 6 — no.

Wait — let's try to see if it's a cycle of three: 17, 18, 6, then 17, 18, 6 — but then pos 4 = 17, pos 5 = 18, pos 6 = 6 — but pos 5 is 18, pos 6 is 6 — so pos 4 = 17?

Then sequence: 17, 18, 6, 17, 18, 6

But pos 4 = 17, pos 5 = 18, pos 6 = 6 — matches.

So is the pattern: 17, 18, 6 repeating?

Then:
- 1: 17
- 2: 18
- 3: 6
- 4: 17
- 5: 18
- 6: 6

Yes! And that matches the given values:
- pos 5: 18 ✓
- pos 6: 6 ✓

So missing number at pos 4 is 17

✔ So answer: 17

That makes sense now.

So the pattern is 17, 18, 6 repeating.

- 1: 17
- 2: 18
- 3: 6
- 4: 17
- 5: 18
- 6: 6

Perfect.

---

Final Answers:

1. 10
2. 9, 11
3. 14, 23
4. 12, 9
5. 69, 66
6. 55, 44
7. 13
8. 17

---

✔ Complete Solutions:

1. 2, 4, 6, 8, 10, 12
2. 3, 5, 7, 9, 11, 13
3. 8, 11, 14, 17, 20, 23
4. 18, 15, 12, 9, 6, 3
5. 75, 72, 69, 66, 63, 60
6. 88, 77, 66, 55, 44, 33
7. 9, 13, 9, 13, 9, 13
8. 17, 18, 6, 17, 18, 6

All patterns solved!