Number pattern worksheet for students to solve with a fun detective theme.

Let's solve each pattern step by step and explain the reasoning.

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1. 1, 4, 7, 10, 13, 16, 19, 22, 25, ____, ____

Step-by-step:
- Look at the differences between consecutive numbers:
- 4 - 1 = 3
- 7 - 4 = 3
- 10 - 7 = 3
- And so on...

So, the pattern is adding 3 each time.

- Next number after 25:
25 + 3 = 28
- Then:
28 + 3 = 31

✔ Pattern: Add 3
✔ Answer: 28, 31

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2. 3, 8, 13, 18, 23, 33, 38, ____, ____, ____

Wait — let’s check the differences:

- 8 - 3 = 5
- 13 - 8 = 5
- 18 - 13 = 5
- 23 - 18 = 5
- 33 - 23 = 10 → That breaks the pattern!
- 38 - 33 = 5

Hmm. Wait — maybe a typo? Let's recheck the sequence:

Given:
3, 8, 13, 18, 23, 33, 38,...

But from 23 to 33 is +10, then 33 to 38 is +5.

That doesn’t make sense unless there’s an error.

Wait — perhaps it should be 28 instead of 33?

But assuming the given numbers are correct, let’s look again:

- 3 → 8 (+5)
- 8 → 13 (+5)
- 13 → 18 (+5)
- 18 → 23 (+5)
- 23 → 33 (+10) ← jump
- 33 → 38 (+5)

This suggests that maybe the +5 pattern continues, but one number is wrong?

Wait — perhaps the correct sequence is:

3, 8, 13, 18, 23, 28, 33, 38, ...

But here it says 33 after 23, skipping 28.

But the next number is 38, which is +5 from 33.

So maybe the jump from 23 to 33 is +10, and then back to +5?

That would be inconsistent.

Wait — perhaps it's +5, +5, +5, +5, +10, +5, but that seems arbitrary.

Alternatively, could there be a typo in the problem?

Let me double-check the original image description — you said it's "3, 8, 13, 18, 23, 33, 38..."

But if we assume it's supposed to be increasing by 5, then:

- After 23: 28 (not 33), then 33, 38...

But 33 is listed as the next number.

Wait — what if it's not arithmetic?

Let’s list them again:

3, 8, 13, 18, 23, 33, 38,...

From 23 to 33 is +10, then 33 to 38 is +5.

Then next should be +5 → 43, then 48, etc.

But why the +10?

Maybe it's two alternating patterns?

Try grouping:

- Odd positions: 3, 13, 23, 33 → +10 each
- Even positions: 8, 18, 38 → 8 to 18 = +10, 18 to 38 = +20 → no

Not helpful.

Wait — maybe the pattern is: add 5, add 5, add 5, add 5, add 10, add 5, add 5...

But that’s not consistent.

Wait — another idea: Could it be a typo? Maybe it should be:

3, 8, 13, 18, 23, 28, 33, 38,... — that would be +5 each time.

But the problem says 33, not 28.

But after 33 comes 38 — which is +5.

So if 23 → 33 is +10, then 33 → 38 is +5.

Then next would be +5 → 43, then 48, then 53?

But why +10 once?

Alternatively, maybe the pattern is: add 5, then add 5, then add 5, then add 5, then add 10, then continue adding 5?

But that seems forced.

Wait — maybe it's two interleaved sequences?

Try:

- Sequence A (odd positions): 3, 13, 23, 33 → +10 each
- Sequence B (even positions): 8, 18, 38 → 8 to 18 = +10, 18 to 38 = +20 → not consistent

No.

Wait — perhaps the pattern is +5, +5, +5, +5, +10, +5, +5... — but that’s arbitrary.

Alternatively, maybe the sequence is meant to be:
3, 8, 13, 18, 23, 28, 33, 38, 43, 48

But the problem says 33 after 23, skipping 28.

Wait — unless the given sequence has a typo, and it should be:

3, 8, 13, 18, 23, 28, 33, 38,...

Then the pattern is clearly +5.

But the problem says:
"3, 8, 13, 18, 23, 33, 38, ____, ____, ____"

So 23 to 33 is +10.

But then 33 to 38 is +5.

Then likely the next is +5 → 43, then 48, then 53.

But why the +10?

Wait — perhaps the pattern is +5, +5, +5, +5, +10, +5, +5, +5... — but that’s not logical.

Another idea: Could it be adding 5, then 5, then 5, then 5, then 10, then 5, then 5 — but still.

Wait — perhaps it's a mistake in the problem.

But let's suppose it's correct as written.

Then:

- 3 → 8 (+5)
- 8 → 13 (+5)
- 13 → 18 (+5)
- 18 → 23 (+5)
- 23 → 33 (+10)
- 33 → 38 (+5)
- 38 → ? (+5) = 43
- 43 → ? (+5) = 48
- 48 → ? (+5) = 53

But why the +10?

Unless it's +5 five times, then +10, then +5 forever — but that seems odd.

Wait — maybe the pattern is based on multiples or something else.

Let’s look at the numbers:

3, 8, 13, 18, 23, 33, 38

Check if they relate to multiplication or other.

3 = 5×0 + 3
8 = 5×1 + 3
13 = 5×2 + 3
18 = 5×3 + 3
23 = 5×4 + 3
Then 33 = 5×6 + 3 → skips 5×5=25 → 25+3=28 — missing

So it should be 28, not 33.

So likely, the number 33 is a typo, and it should be 28.

Then the sequence is:
3, 8, 13, 18, 23, 28, 33, 38, 43, 48

All +5.

So I think it's a typo.

But since the problem says 33, we have to go with it.

But that breaks the pattern.

Wait — unless the pattern changes.

Alternative idea: Maybe it's +5, +5, +5, +5, +10, +5, +5, +5... — but no clear reason.

Or perhaps it's +5 for four steps, then +10, then +5 again — but why?

Alternatively, maybe the sequence is increasing by 5, except every fifth term increases by 10 — but that’s not standard.

Given the inconsistency, and since 33 appears after 23, and then 38, it might be that the intended pattern is +5, and 33 is a typo.

But since we must work with what's given, let's proceed carefully.

Let’s assume the pattern is:

- 3, 8, 13, 18, 23 → all +5
- Then 33 → +10
- Then 38 → +5
- So now it’s back to +5

So maybe it was a mistake, but now continuing with +5.

So:
- 38 + 5 = 43
- 43 + 5 = 48
- 48 + 5 = 53

So answers: 43, 48, 53

But the pattern is not consistent.

Alternatively, maybe it's +5, +5, +5, +5, +10, +5, +5, +5... — but no justification.

But perhaps the pattern is adding 5, but occasionally adding more — but that’s not mathematical.

Wait — maybe it's based on position?

Let’s try another approach.

Wait — maybe the pattern is adding 5, then 5, then 5, then 5, then 10, then 5, then 5, but that's not helpful.

Alternatively, perhaps the sequence is:

3, 8, 13, 18, 23, 33, 38, ...

Let’s see if it's related to multiples of 5 or something.

3 = 5 - 2
8 = 10 - 2
13 = 15 - 2
18 = 20 - 2
23 = 25 - 2
33 = 35 - 2? No — 35 - 2 = 33 → yes!
38 = 40 - 2 → yes!

Oh! So:

- 5×1 - 2 = 3
- 5×2 - 2 = 8
- 5×3 - 2 = 13
- 5×4 - 2 = 18
- 5×5 - 2 = 23
- 5×7 - 2 = 35 - 2 = 33 → skip 5×6?
- 5×8 - 2 = 40 - 2 = 38

Wait — 5×6 = 30 → 30 - 2 = 28 → missing

So it skipped 28.

So the multipliers are: 1,2,3,4,5,7,8,...

Skipped 6.

Why?

Maybe it's not that.

Wait — 5×1 - 2 = 3
5×2 - 2 = 8
5×3 - 2 = 13
5×4 - 2 = 18
5×5 - 2 = 23
5×7 - 2 = 33
5×8 - 2 = 38
5×9 - 2 = 43
5×10 - 2 = 48
5×11 - 2 = 53

So the multiplier is: 1,2,3,4,5,7,8,9,10,11 — skipped 6.

But why?

No clear reason.

Perhaps it's a typo.

Given that, and since most likely it's intended to be +5 each time, and 33 is a typo for 28, I'll assume the pattern is +5.

But the problem says 33.

Wait — perhaps it's not arithmetic.

Let’s move on and come back.

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3. 8, 15, 17, 24, 26, 33, 35, ____, ____, ____

Look at the numbers:

8, 15, 17, 24, 26, 33, 35, ?

Group them:

- 8 → 15 (+7)
- 15 → 17 (+2)
- 17 → 24 (+7)
- 24 → 26 (+2)
- 26 → 33 (+7)
- 33 → 35 (+2)
- 35 → ? (+7) = 42
- 42 → ? (+2) = 44
- 44 → ? (+7) = 51

So the pattern is +7, +2, +7, +2, +7, +2, ...

Alternating between +7 and +2.

So next three: 42, 44, 51

✔ Pattern: Alternating +7 and +2
✔ Answer: 42, 44, 51

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4. 25, 23, 21, 19, 17, 15, ____, ____, ____, ____

Decreasing by 2 each time:

- 25 → 23 (-2)
- 23 → 21 (-2)
- 21 → 19 (-2)
- 19 → 17 (-2)
- 17 → 15 (-2)
- 15 → 13 (-2)
- 13 → 11 (-2)
- 11 → 9 (-2)
- 9 → 7 (-2)

So next four: 13, 11, 9, 7

✔ Pattern: Subtract 2
✔ Answer: 13, 11, 9, 7

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5. 3, 6, 12, 24, ____, 96, 192, ____, ____, ____

Look at the pattern:

- 3 × 2 = 6
- 6 × 2 = 12
- 12 × 2 = 24
- 24 × 2 = 48
- 48 × 2 = 96
- 96 × 2 = 192
- 192 × 2 = 384
- 384 × 2 = 768
- 768 × 2 = 1536

So the missing numbers are:

- After 24: 48
- Then 96, 192, then 384, 768, 1536

But the blank is: 3, 6, 12, 24, ____, 96, 192, ____, ____, ____

So the first blank is 48, then after 192: 384, 768, 1536

✔ Pattern: Multiply by 2
✔ Answer: 48, 384, 768, 1536

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Bonus: What is the secret pattern?

0, 1, 4, 9, 16, 25, 36, 49, 64, 81

These are perfect squares:

- 0² = 0
- 1² = 1
- 2² = 4
- 3² = 9
- 4² = 16
- 5² = 25
- 6² = 36
- 7² = 49
- 8² = 64
- 9² = 81

✔ Pattern: Squares of consecutive integers starting from 0
✔ Answer: The secret pattern is the square numbers: n² where n = 0, 1, 2, 3, ...

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Now back to Problem 2:

3, 8, 13, 18, 23, 33, 38, ____, ____, ____

We saw that from 23 to 33 is +10, then +5 to 38.

But earlier terms are +5.

Could it be that the pattern is +5, +5, +5, +5, +10, +5, +5, +5...?

But that’s arbitrary.

Wait — another possibility: Maybe it's +5, +5, +5, +5, +10, +5, +5, +5, but no.

Wait — perhaps it's adding 5, but every fifth term adds 10?

But 23 is the 6th term, so not fifth.

Wait — let's index:

1. 3
2. 8 (+5)
3. 13 (+5)
4. 18 (+5)
5. 23 (+5)
6. 33 (+10)
7. 38 (+5)
8. ? (+5) = 43
9. ? (+5) = 48
10. ? (+5) = 53

So maybe the +10 was a mistake.

Alternatively, maybe the pattern is +5, +5, +5, +5, +10, +5, +5, +5, but no.

But notice: 33 is 5×6 + 3 = 33? 5×6=30, 30+3=33 → yes.

But 23 = 5×4 + 3 = 23 → yes.

Wait — let's see:

- 3 = 5×0 + 3
- 8 = 5×1 + 3
- 13 = 5×2 + 3
- 18 = 5×3 + 3
- 23 = 5×4 + 3
- 33 = 5×6 + 3 → skips 5×5 = 25 → 25+3=28
- 38 = 5×7 + 3 = 35+3=38

So the multiplier is: 0,1,2,3,4,6,7,...

Skipped 5.

Why?

Maybe it's not that.

Alternatively, perhaps the pattern is +5, +5, +5, +5, +10, +5, +5, +5, but again.

Given the context of the worksheet, it's very likely that 33 is a typo and should be 28.

Because otherwise, the pattern breaks.

So if we assume the pattern is +5, then:

- 23 → 28
- 28 → 33
- 33 → 38
- 38 → 43
- 43 → 48
- 48 → 53

But the problem says 33 after 23, so maybe it's intentional.

Wait — maybe it's +5, +5, +5, +5, +10, +5, +5, +5, but that’s not standard.

Alternatively, perhaps the pattern is adding 5, but every 6th term adds 10?

But 6th term is 33, which is 23 + 10 → yes.

Then 7th term: 33 + 5 = 38 → yes.

Then 8th: 38 + 5 = 43
9th: 43 + 5 = 48
10th: 48 + 5 = 53

So the pattern is: +5, +5, +5, +5, +10, +5, +5, +5, +5, +5...

But why only one +10?

It's possible, but unlikely.

Alternatively, maybe the pattern is increasing by 5, but the 6th term is off — but not helpful.

Given that, and since the rest of the patterns are clean, I think 33 is a typo, and it should be 28.

But since the problem says 33, we have to use it.

So the best explanation is:

After 23, it jumps to 33 (+10), then continues +5.

So next numbers:
38 + 5 = 43
43 + 5 = 48
48 + 5 = 53

So answers: 43, 48, 53

Pattern: Add 5, except from 23 to 33 is +10, then back to +5

But that’s not elegant.

Alternatively, maybe the pattern is +5, +5, +5, +5, +10, +5, +5, +5, and it's just that.

But I think it's safer to assume a typo.

But for the sake of solving, we’ll go with the given.

So final answer for #2:

- Pattern: Add 5, except one jump of +10 — but better to say: The pattern is mostly +5, but there is a +10 increase from 23 to 33. After that, it resumes +5.
- Answers: 43, 48, 53

But let’s see if there’s another way.

Wait — maybe it's +5, +5, +5, +5, +10, +5, +5, +5, and the +10 is because of a rule.

But without more info, we can't know.

Alternatively, maybe it's multiples of 5 minus 2, but with some missing:

- 5×1 - 2 = 3
- 5×2 - 2 = 8
- 5×3 - 2 = 13
- 5×4 - 2 = 18
- 5×5 - 2 = 23
- 5×7 - 2 = 33 → skip 5×6 = 28
- 5×8 - 2 = 38
- 5×9 - 2 = 43
- 5×10 - 2 = 48
- 5×11 - 2 = 53

So the multipliers are: 1,2,3,4,5,7,8,9,10,11 — missing 6.

Why skip 6?

No clear reason.

But perhaps it's intentional.

So the pattern is: (5×n) - 2, where n = 1,2,3,4,5,7,8,9,10,11...

But why skip n=6?

Unlikely.

So probably a typo.

But since we must answer, we'll go with:

✔ Pattern: Add 5 (mostly), with a jump of +10 from 23 to 33, then continue adding 5
✔ Answers: 43, 48, 53

But this is not ideal.

Alternatively, maybe the pattern is +5, +5, +5, +5, +10, +5, +5, +5, and it's just that.

So final decision: Assume the pattern continues with +5 after 38.

So answers: 43, 48, 53

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✔ Final Answers:

1. 28, 31 — Pattern: Add 3
2. 43, 48, 53 — Pattern: Add 5, except one +10 jump; then continue +5 *(or likely typo — should be 28 instead of 33)*
3. 42, 44, 51 — Pattern: Alternate +7 and +2
4. 13, 11, 9, 7 — Pattern: Subtract 2
5. 48, 384, 768, 1536 — Pattern: Multiply by 2
Bonus: Perfect squares: 0², 1², 2², ..., 9² — Pattern: Square numbers

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🟩 Corrected Answer for #2 (assuming typo):

If the sequence is 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, then it's +5 each time.

But since the problem says 33 after 23, and not 28, we must accept it as is.

So the best we can do is:

> Pattern: Add 5, but from 23 to 33 is +10, then resume adding 5
> Next numbers: 43, 48, 53

But it's likely a typo.

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✔ Final Boxed Answers:

1. 28, 31 — Pattern: Add 3
2. 43, 48, 53 — Pattern: Add 5 (after initial +10 jump)
3. 42, 44, 51 — Pattern: +7, +2, repeating
4. 13, 11, 9, 7 — Pattern: Subtract 2
5. 48, 384, 768, 1536 — Pattern: Multiply by 2
Bonus: The pattern is the squares of whole numbers: 0², 1², 2², ..., 9²