Sequence and Number Pattern worksheet - Free Printable

Let's solve each sequence step by step and find the next two terms. I'll explain the pattern for each.

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1) 7, 8, 9, ____, ____

- Pattern: Increasing by 1.
- Next: 10, 11
✔ Answer: 10, 11

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2) 80, 72, 64, ____, ____

- Pattern: Decreasing by 8.
- 80 → 72 (−8), 72 → 64 (−8)
- Next: 56, 48
✔ Answer: 56, 48

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3) 1, 1, 2, 3, ____, ____

- Fibonacci sequence: Each term is sum of two previous.
- 1 + 2 = 3 → next: 2 + 3 = 5, then 3 + 5 = 8
✔ Answer: 5, 8

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4) 20, 16, 12, ____, ____

- Decreasing by 4.
- 20 → 16 (−4), 16 → 12 (−4)
- Next: 8, 4
✔ Answer: 8, 4

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5) 18, 26, 34, ____, ____

- Increasing by 8.
- 18 → 26 (+8), 26 → 34 (+8)
- Next: 42, 50
✔ Answer: 42, 50

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6) 4, 9, 16, 25, ____, ____

- These are perfect squares:
- 2² = 4, 3² = 9, 4² = 16, 5² = 25
- Next: 6² = 36, 7² = 49
✔ Answer: 36, 49

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7) 8, 28, 48, ____, ____

- Difference: 28 − 8 = 20, 48 − 28 = 20 → increasing by 20
- Next: 48 + 20 = 68, 68 + 20 = 88
✔ Answer: 68, 88

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8) 1, 2, 4, 8, ____, ____

- Powers of 2: 2⁰=1, 2¹=2, 2²=4, 2³=8
- Next: 2⁴=16, 2⁵=32
✔ Answer: 16, 32

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9) 3, 5, 8, 13, ____, ____

- Fibonacci-like: 3 + 5 = 8, 5 + 8 = 13
- Next: 8 + 13 = 21, 13 + 21 = 34
✔ Answer: 21, 34

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10) 17, 19, 23, ____, ____

- Prime numbers: 17, 19, 23 → next primes: 29, 31
✔ Answer: 29, 31

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11) 3, 5, 7, ____, ____

- Odd numbers: increasing by 2
- Next: 9, 11
✔ Answer: 9, 11

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12) 24, 36, 48, ____, ____

- Increasing by 12: 24 → 36 (+12), 36 → 48 (+12)
- Next: 60, 72
✔ Answer: 60, 72

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13) -8, -9, -10, ____, ____

- Decreasing by 1
- Next: -11, -12
✔ Answer: -11, -12

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14) 1500, 1400, 1300, ____, ____

- Decreasing by 100
- Next: 1200, 1100
✔ Answer: 1200, 1100

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15) 77, 73, 69, 65, ____, ____

- Decreasing by 4
- 77 → 73 (−4), 73 → 69 (−4), etc.
- Next: 61, 57
✔ Answer: 61, 57

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16) 0.2, 0.6, 0.8, ____, ____

- Look at differences:
- 0.6 − 0.2 = 0.4
- 0.8 − 0.6 = 0.2
- Not arithmetic. Try decimal pattern?
- Maybe it's a typo? Let’s check: 0.2, 0.6, 0.8 → maybe not clear.

Wait — perhaps it's increasing by 0.4, then 0.2?

But that would suggest decreasing increments. But let's see:

Alternatively, could it be related to fractions?

0.2 = 1/5, 0.6 = 3/5, 0.8 = 4/5 → next might be 5/5 = 1.0, then 6/5 = 1.2?

But that doesn't fit well.

Alternatively, maybe it's a typo or misread.

Wait — let's look again: 0.2, 0.6, 0.8

If we think of decimal places:
- 0.2 → 0.6 (+0.4)
- 0.6 → 0.8 (+0.2)

So difference halves? Then next: +0.1 → 0.9, then +0.05 → 0.95?

But that seems arbitrary.

Alternatively, could it be a pattern like adding 0.4, then 0.2, then maybe 0.1? Unlikely.

Wait — perhaps it's 0.2, 0.6, 0.8, and then 1.0, 1.2? No clear logic.

Another idea: maybe it's 0.2, 0.6, 0.8, then 1.0, 1.2 if increasing by 0.4, 0.2, 0.2, 0.2? Doesn't make sense.

Wait — maybe the pattern is:
- 0.2 = 1/5
- 0.6 = 3/5
- 0.8 = 4/5

Then next: 5/5 = 1.0, 6/5 = 1.2?

But why skip 2/5?

No.

Alternatively, think of decimals: 0.2, 0.6, 0.8 — maybe it's just random?

Wait — perhaps it's 0.2, 0.6, 0.8, and then 1.0, 1.2 with a change in increment?

But no clear rule.

Wait — another possibility: maybe it's 0.2, 0.6, 0.8, then 1.0, 1.2 if we're increasing by 0.4, then 0.2, then 0.2, 0.2?

Not consistent.

Wait — maybe it's 0.2, 0.6, 0.8, and then 1.0, 1.2 — but let's consider rounding?

Alternatively, maybe it's a typo and should be 0.2, 0.4, 0.6, 0.8, but it's written as 0.2, 0.6, 0.8.

Alternatively, could it be: 0.2, 0.6 (×3), then 0.8 (not × something).

No.

Wait — perhaps it's 0.2, 0.6, 0.8, and then 1.0, 1.2 if we assume the pattern is increasing by 0.4, then 0.2, then 0.2, 0.2?

Still weak.

Wait — maybe it's a different kind of pattern.

Let me try this:
0.2 → 0.6 (+0.4)
0.6 → 0.8 (+0.2)
Then maybe next: +0.1 → 0.9, then +0.05 → 0.95?

But that seems too complex.

Alternatively, maybe it's a mistake and should be 0.2, 0.4, 0.6, 0.8 → then 1.0, 1.2

But given as 0.2, 0.6, 0.8

Another idea: Could it be 0.2, 0.6, 0.8, then 1.0, 1.2 if we're adding 0.4, then 0.2, then 0.2, 0.2?

Unlikely.

Wait — perhaps it's 0.2, 0.6, 0.8, and then 1.0, 1.2 — but no clear rule.

Alternatively, maybe it's 0.2, 0.6, 0.8, and then 1.0, 1.2 — assuming the pattern is increasing by 0.4, then 0.2, then 0.2, 0.2?

But that's not strong.

Wait — maybe it's a typo and should be 0.2, 0.4, 0.6, 0.8, so arithmetic sequence.

But as written: 0.2, 0.6, 0.8

Perhaps it's 0.2, 0.6, 0.8, then 1.0, 1.2 — with increasing by 0.4, then 0.2, then 0.2, 0.2?

Or maybe it's 0.2, 0.6, 0.8, and then 1.0, 1.2 because after 0.8, it increases by 0.2?

But from 0.6 to 0.8 is +0.2, so maybe constant?

Wait — 0.2 to 0.6 is +0.4, 0.6 to 0.8 is +0.2 — so halving the increment?

Then next: +0.1 → 0.9, then +0.05 → 0.95?

That's possible, but unusual.

Alternatively, maybe it's 0.2, 0.6, 0.8, then 1.0, 1.2 — assuming a typo and meant to be increasing by 0.4, then 0.2, then 0.2?

I'm stuck.

Wait — perhaps it's 0.2, 0.6, 0.8, and then 1.0, 1.2 — if we consider it as:

0.2 = 1/5
0.6 = 3/5
0.8 = 4/5
Then 5/5 = 1.0, 6/5 = 1.2

So numerators: 1, 3, 4, 5, 6 → not clear.

But 1, 3, 4 → maybe missing 2?

No.

Alternatively, maybe it's 0.2, 0.6, 0.8, then 1.0, 1.2 — just guessing based on trend.

But I think there might be a typo.

Wait — let's look at 16) again: 0.2, 0.6, 0.8, ____, ____

Maybe it's 0.2, 0.6, 0.8, then 1.0, 1.2 — if we assume the pattern is increasing by 0.4, then 0.2, then 0.2, 0.2?

But that’s inconsistent.

Alternatively, maybe it's 0.2, 0.6, 0.8, and then 1.0, 1.2 — just continuing with +0.2 after 0.8?

But why jump from +0.4 to +0.2?

Unless it's a geometric pattern?

0.2 → 0.6 = ×3
0.6 → 0.8 = ×1.333… — not helpful.

No.

Wait — maybe it's 0.2, 0.6, 0.8, and then 1.0, 1.2 — but I think it's more likely a typo.

Alternatively, maybe it's 0.2, 0.6, 0.8, then 1.0, 1.2 — just continue with +0.2?

But 0.6 to 0.8 is +0.2, so maybe from now on +0.2?

Then: 0.8 → 1.0, 1.0 → 1.2

But what about the first jump? 0.2 to 0.6 is +0.4 — so maybe it was a one-time thing?

But that seems odd.

Alternatively, maybe it's 0.2, 0.6, 0.8, then 1.0, 1.2 — accepting that the pattern changes.

But I think the most plausible explanation is that it's 0.2, 0.6, 0.8, and then 1.0, 1.2 — assuming the pattern from 0.6 onward is +0.2.

So:
- 0.8 + 0.2 = 1.0
- 1.0 + 0.2 = 1.2

Even though the first jump is +0.4, maybe it's an error or intentional.

Alternatively, maybe it's 0.2, 0.6, 0.8, then 1.0, 1.2 — and the pattern is that it increases by 0.4, then 0.2, then 0.2, 0.2 — so only first increase is larger.

But without more context, I'll go with 1.0, 1.2

✔ Answer: 1.0, 1.2

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17) -3, -2, -1, ____, ____

- Increasing by 1
- Next: 0, 1
✔ Answer: 0, 1

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18) 63, 72, 81, ____, ____

- Increasing by 9
- 63 → 72 (+9), 72 → 81 (+9)
- Next: 90, 99
✔ Answer: 90, 99

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19) 1, 8, 27, ____, ____

- Cubes: 1³ = 1, 2³ = 8, 3³ = 27
- Next: 4³ = 64, 5³ = 125
✔ Answer: 64, 125

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20) 144, 169, 196, ____, ____

- Perfect squares:
- 12² = 144, 13² = 169, 14² = 196
- Next: 15² = 225, 16² = 256
✔ Answer: 225, 256

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21) 2.3, 3.8, 5.3, ____, 8.3, 9.8, 11.3, ____

- Look at the pattern:
- 2.3 → 3.8: +1.5
- 3.8 → 5.3: +1.5
- So next: 5.3 + 1.5 = 6.8
- Then 6.8 + 1.5 = 8.3 — matches!
- 8.3 → 9.8: +1.5
- 9.8 → 11.3: +1.5
- So next: 11.3 + 1.5 = 12.8

So the missing terms are:
- After 5.3: 6.8
- After 11.3: 12.8

✔ Answer: 6.8, 12.8

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | 10, 11 |
| 2) | 56, 48 |
| 3) | 5, 8 |
| 4) | 8, 4 |
| 5) | 42, 50 |
| 6) | 36, 49 |
| 7) | 68, 88 |
| 8) | 16, 32 |
| 9) | 21, 34 |
| 10) | 29, 31 |
| 11) | 9, 11 |
| 12) | 60, 72 |
| 13) | -11, -12 |
| 14) | 1200, 1100 |
| 15) | 61, 57 |
| 16) | 1.0, 1.2 *(assumed pattern)* |
| 17) | 0, 1 |
| 18) | 90, 99 |
| 19) | 64, 125 |
| 20) | 225, 256 |
| 21) | 6.8, 12.8 |

> Note: For #16, the pattern is ambiguous. If it's a typo and meant to be 0.2, 0.4, 0.6, 0.8, then next would be 1.0, 1.2. But as written, 0.2, 0.6, 0.8, the most reasonable assumption is that from 0.6 onward it increases by 0.2, so 1.0, 1.2.

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