Number sequence worksheet for practicing pattern recognition with fun octopus graphics.

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

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1. 2, 4, 6, 8, ____, ____, ____

- Pattern: Each number increases by 2.
- Next numbers: 10, 12, 14
- ✔ Answer: 10, 12, 14

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2. 3, 6, 9, 12, ____, ____, ____

- Pattern: Increases by 3.
- Next numbers: 15, 18, 21
- ✔ Answer: 15, 18, 21

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3. 6, 7, 9, 11, ____, ____, ____

- Let's look at the differences:
- 7 – 6 = 1
- 9 – 7 = 2
- 11 – 9 = 2
- So far: +1, +2, +2 → maybe alternating or increasing?
- But wait — let’s check if it's related to odd numbers or something else.
- Alternatively, think about adding odd numbers: 1, then 2, then 2...
- Not clear yet. Let's try another idea.

Wait — perhaps it's adding consecutive odd numbers, but not quite.

Alternatively, look at the positions:

- 6 (start)
- 6 + 1 = 7
- 7 + 2 = 9
- 9 + 2 = 11
- Then maybe +3? → 11 + 3 = 14
- Then +3? → 14 + 3 = 17
- Then +4? → 17 + 4 = 21?

But that seems inconsistent.

Wait — maybe it's adding 1, then 2, then 2, then 3, then 3, then 4...?

But that’s speculative.

Alternatively, is there a different pattern?

Let’s list them again:
6, 7, 9, 11

Differences: +1, +2, +2

Maybe next difference is +3, then +3, then +4?

So:
- 11 + 3 = 14
- 14 + 3 = 17
- 17 + 4 = 21

But this is guesswork.

Wait — could it be skipping even numbers?

6, 7, 9, 11 — all are increasing, skipping some.

From 6 to 7: +1
7 to 9: +2
9 to 11: +2
Now, maybe +3 → 14
Then +3 → 17
Then +4 → 21?

Still unclear.

Alternatively, consider that 6, 7, 9, 11 might be all numbers starting from 6, but only including numbers that are not divisible by 4 or something?

No.

Another idea: perhaps it's adding 1, then 2, then 2, then 3, then 3, then 4… — like increasing every two steps?

But that’s not standard.

Wait — let's try a different approach.

Look at the numbers: 6, 7, 9, 11

What if it's adding odd numbers: +1, +2, +2? No.

Wait — what if it's increasing by 1, then 2, then 2, then 3, then 3, then 4...?

But that's not common.

Alternatively, maybe it's adding the next odd number after 1?

Wait — let’s see:

6
6 + 1 = 7
7 + 2 = 9
9 + 2 = 11
11 + 3 = 14
14 + 3 = 17
17 + 4 = 21

That gives: 14, 17, 21

But why?

Perhaps the pattern is: add 1, then add 2 twice, then add 3 twice, then add 4 twice?

But we only have four terms.

So:
- 6 → 7 (+1)
- 7 → 9 (+2)
- 9 → 11 (+2)
- 11 → 14 (+3)
- 14 → 17 (+3)
- 17 → 20 (+3)? Wait no.

Wait — maybe it's adding 1, then 2, then 2, then 3, then 3, then 4, etc., but that would be:

6
+1 → 7
+2 → 9
+2 → 11
+3 → 14
+3 → 17
+4 → 21

So: 14, 17, 21

But is there a better reason?

Alternatively, could it be every number except multiples of 4? 6,7,9,11 — yes, skips 8,10? But 8 and 10 are skipped, but 12 is also skipped.

Not helpful.

Wait — another idea: prime numbers? 6 is not prime, 7 is, 9 isn't, 11 is — so no.

Back to differences: +1, +2, +2 → maybe next is +3, +3, +4?

But without more info, hard to say.

Wait — perhaps it's adding the sequence: 1, 2, 2, 3, 3, 4, 4,...?

So:
- 6 + 1 = 7
- 7 + 2 = 9
- 9 + 2 = 11
- 11 + 3 = 14
- 14 + 3 = 17
- 17 + 4 = 21

Yes — so the increments are: 1, 2, 2, 3, 3, 4, 4...

So the pattern is: start with 6, then add increasing integers, with each integer repeated twice, starting from 1.

So:
- Add 1 → 7
- Add 2 → 9
- Add 2 → 11
- Add 3 → 14
- Add 3 → 17
- Add 4 → 21

✔ So answer: 14, 17, 21

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4. 20, 30, 40, 50, ____, ____, ____

- Increases by 10.
- Next: 60, 70, 80
- ✔ Answer: 60, 70, 80

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5. 100, 90, 80, 70, ____, ____, ____

- Decreases by 10.
- Next: 60, 50, 40
- ✔ Answer: 60, 50, 40

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6. 24, 21, 18, 15, ____, ____, ____

- Decreases by 3.
- 24 – 3 = 21, 21 – 3 = 18, 18 – 3 = 15
- Next: 12, 9, 6
- ✔ Answer: 12, 9, 6

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7. 360, 300, 250, 200, ____, ____, ____

- Differences:
- 360 – 300 = 60
- 300 – 250 = 50
- 250 – 200 = 50

Wait — first drop is 60, then 50, then 50?

Not consistent.

Wait: 360 → 300 (–60), 300 → 250 (–50), 250 → 200 (–50)

So maybe next is –50 again?

Then:
- 200 – 50 = 150
- 150 – 50 = 100
- 100 – 50 = 50

But why did it drop by 60 first?

Is it possible the pattern is: subtract 60, then subtract 50 repeatedly?

But that seems arbitrary.

Wait — maybe it's decreasing by multiples?

Or perhaps it's subtracting 60, then 50, then 50, then 50...?

But why?

Alternatively, look at the numbers:

360, 300, 250, 200

360 → 300: –60
300 → 250: –50
250 → 200: –50

So maybe the first decrease is larger, then it stabilizes at –50?

So continue with –50:
- 200 – 50 = 150
- 150 – 50 = 100
- 100 – 50 = 50

✔ Answer: 150, 100, 50

But why start with –60?

Maybe typo? Or intentional?

Alternatively, could it be based on multiplication?

360 ÷ 1.2 = 300
300 ÷ 1.2 = 250? 300 ÷ 1.2 = 250 → yes!
250 ÷ 1.25 = 200? 250 ÷ 1.25 = 200 → yes!

Wait — not consistent.

But 360 → 300: × 5/6
300 → 250: × 5/6? 300 × 5/6 = 250 → yes
250 × 5/6 ≈ 208.33 → not 200

No.

Wait — 360 → 300: –60
300 → 250: –50
250 → 200: –50

So maybe: –60, then –50, –50, –50...

So likely continues with –50.

Thus: 150, 100, 50

✔ Answer: 150, 100, 50

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8. 27, 31, 36, 39, ____, ____, ____

- Differences:
- 31 – 27 = 4
- 36 – 31 = 5
- 39 – 36 = 3

Not obvious.

Wait: +4, +5, +3

Maybe alternating?

Try: +4, +5, +3, +4, +5, +3?

Then:
- 39 + 4 = 43
- 43 + 5 = 48
- 48 + 3 = 51

But that's just guessing.

Alternatively, think of digits or something else.

Wait — maybe it's related to letters? 27, 31, 36, 39 — not sure.

Another idea: maybe it's increasing by 4, 5, 3 — but no clear pattern.

Wait — could it be that the number of letters in the word for the number?

27: "twenty-seven" — 11 letters
31: "thirty-one" — 10 letters — no

Not helpful.

Wait — maybe it's adding 4, then 5, then 3, then 4, then 5, then 3?

But why?

Alternatively, look at the values:

27, 31, 36, 39

Could it be multiples of 3?

27 = 9×3, 31 not multiple of 3, so no.

Wait — differences: +4, +5, +3

Maybe it's +4, +5, +3, +4, +5, +3?

So:
- 39 + 4 = 43
- 43 + 5 = 48
- 48 + 3 = 51

So: 43, 48, 51

But why?

Alternatively, think of addition pattern:

27 → 31: +4
31 → 36: +5
36 → 39: +3

Now, maybe next is +4, +5, +3?

Yes — repeating cycle: +4, +5, +3

So:
- 39 + 4 = 43
- 43 + 5 = 48
- 48 + 3 = 51

✔ Answer: 43, 48, 51

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9. 20, 16, 17, 16, ____, ____, ____

- Sequence: 20, 16, 17, 16, ?, ?, ?

Look at it:
- 20 → 16: –4
- 16 → 17: +1
- 17 → 16: –1

So: –4, +1, –1

Then maybe next is +1, –1, +1?

Wait — pattern: –4, +1, –1, +1, –1, +1?

But that doesn’t make sense.

Alternatively, maybe it's alternating between two sequences?

Split into odd and even positions:

- Position 1: 20
- Position 2: 16
- Position 3: 17
- Position 4: 16
- Position 5: ?
- Position 6: ?
- Position 7: ?

Odd positions (1,3,5,7): 20, 17, ?, ?
Even positions (2,4,6): 16, 16, ?

So:
- Odd: 20 → 17 → ? → ? → decreasing by 3? Then maybe 14, 11?
- Even: 16, 16 → constant?

So:
- Position 5 (odd): 17 – 3 = 14
- Position 6 (even): 16
- Position 7 (odd): 14 – 3 = 11

So sequence: 20, 16, 17, 16, 14, 16, 11

But is that plausible?

Check: 20, 16, 17, 16, 14, 16, 11

But why does odd positions go: 20, 17, 14, 11 — decreasing by 3?

And even positions: 16, 16 — stays same?

Possibly.

But let’s see if there’s another way.

Another idea: maybe it's alternating between two patterns:

- First term: 20
- Then 16, then 17, then 16 — so maybe the “16” is a fixed value?

Wait — positions:
1: 20
2: 16
3: 17
4: 16
5: ?
6: ?
7: ?

So maybe every even position is 16?

Then:
- Position 2: 16
- Position 4: 16
- Position 6: 16

So 6th term = 16

Now odd positions:
- 1: 20
- 3: 17
- 5: ?
- 7: ?

So 20 → 17: –3

Then maybe 17 → 14 → 11?

So:
- 5th: 14
- 7th: 11

So sequence: 20, 16, 17, 16, 14, 16, 11

✔ Answer: 14, 16, 11

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10. 110, 105, 100, 95, ____, ____, ____

- Decreases by 5.
- 110 → 105: –5
- 105 → 100: –5
- 100 → 95: –5
- Continue: 90, 85, 80

✔ Answer: 90, 85, 80

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Final Answers:

1. 10, 12, 14
2. 15, 18, 21
3. 14, 17, 21
4. 60, 70, 80
5. 60, 50, 40
6. 12, 9, 6
7. 150, 100, 50
8. 43, 48, 51
9. 14, 16, 11
10. 90, 85, 80

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Summary of Patterns:

1. +2
2. +3
3. Add: +1, +2, +2, +3, +3, +4 → so +3, +3, +4? Wait earlier we said +3, +3, +4? But we used +3, +3, +4 → 14, 17, 21
Actually: 6→7 (+1), 7→9 (+2), 9→11 (+2), 11→14 (+3), 14→17 (+3), 17→21 (+4) → yes
4. +10
5. –10
6. –3
7. –60, then –50, –50, –50 → so –50, –50, –50
8. +4, +5, +3, repeat → +4, +5, +3
9. Odd positions: –3 each time; even positions: 16
10. –5

All solved!