Math worksheet for identifying and continuing number patterns and sequences.

Let's solve each sequence step by step and identify the pattern to find the next two terms.

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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 terms.
- 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, ____, ____

- Squares of consecutive integers:
- 2² = 4, 3² = 9, 4² = 16, 5² = 25
- Next: 6² = 36, 7² = 49
✔ Answer: 36, 49

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7) 8, 28, 48, ____, ____

- Differences: 28 - 8 = 20, 48 - 28 = 20 → increasing by 20
- So: 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 (primes? but not necessarily): 3,5,7 → next odd numbers: 9, 11
- But they are also primes. However, 9 is not prime — so likely just odd numbers.
- So: 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), 69 → 65 (-4)
- Next: 61, 57
✔ Answer: 61, 57

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16) 0.2, 0.6, 0.8, ____, ____

- Let's look at differences:
- 0.6 - 0.2 = 0.4
- 0.8 - 0.6 = 0.2 → decreasing difference?
- Or perhaps decimal pattern?

Wait: 0.2, 0.6, 0.8 → maybe it's increasing in a different way.

Alternatively, think of fractions:
- 0.2 = 1/5, 0.6 = 3/5, 0.8 = 4/5 → next could be 5/5 = 1.0, then 6/5 = 1.2

But that seems arbitrary.

Alternatively, maybe typo or irregular pattern?

Wait: Try another idea:

Is there a pattern like adding decimals?

From 0.2 → 0.6: +0.4
From 0.6 → 0.8: +0.2
So differences: +0.4, +0.2 → maybe next +0.1, +0.05?

But that’s too speculative.

Wait — perhaps it's meant to be:
- 0.2, 0.6, 0.8 → maybe skip some?

Alternatively, think of digits?

Another idea: Maybe it's a typo? Or perhaps it's related to multiples?

Wait — let's try this:

Suppose we write them as tenths:
- 2, 6, 8 → what next?

Maybe: 10, 12 → so 1.0, 1.2?

Then: 0.2, 0.6, 0.8, 1.0, 1.2

But why jump from 0.6 to 0.8? Why not 0.7?

Alternatively, maybe it's based on something else.

Wait — check if it's a known sequence.

Alternatively, suppose the pattern is:
- 0.2, then 0.6 (0.2 + 0.4), then 0.8 (0.6 + 0.2)

Now if we halve the increment: next +0.1 → 0.9, then +0.05 → 0.95?

But that’s not consistent.

Alternatively, maybe it's not arithmetic.

Wait — perhaps it's a typo? Let's consider possibility:

Could it be 0.2, 0.4, 0.6, 0.8, 1.0, 1.2? Then missing 0.4.

But given: 0.2, 0.6, 0.8 → so maybe skip 0.4?

No.

Another idea: Could it be related to decimals where digits increase?

0.2 → 0.6 → 0.8 → next could be 1.0, 1.2?

Or perhaps: 0.2, 0.6, 0.8, 1.0, 1.2?

But why jump from 0.6 to 0.8?

Wait — maybe it's not arithmetic.

Wait — think differently: 0.2, 0.6, 0.8...

What if we add:
- 0.2 + 0.4 = 0.6
- 0.6 + 0.2 = 0.8
- Now, maybe +0.1 = 0.9
- Then +0.05 = 0.95?

Too messy.

Alternatively, perhaps it's 0.2, 0.6, 0.8, 1.0, 1.2 — doubling the increments?

No.

Wait — another thought: Is it possible that this is a typo? Or perhaps it's supposed to be:

0.2, 0.4, 0.6, 0.8 → but it's written as 0.2, 0.6, 0.8 → skipping 0.4?

Unlikely.

Wait — maybe it's 0.2, 0.6, 0.8, then next: 1.0, 1.2? If we assume increasing by 0.2 after 0.6?

But 0.6 to 0.8 is +0.2, so maybe continue +0.2 → 1.0, 1.2?

But 0.2 to 0.6 is +0.4, then +0.2 → inconsistent.

Unless it's: +0.4, then +0.2, then +0.1, +0.05?

No.

Wait — perhaps it's 0.2, 0.6, 0.8, 1.0, 1.2 — meaning it increases by 0.4, then 0.2, then 0.2, then 0.2?

That would make sense: 0.2 → 0.6 (+0.4), then 0.6 → 0.8 (+0.2), then 0.8 → 1.0 (+0.2), 1.0 → 1.2 (+0.2)

So maybe the first jump is larger, then stabilizes?

But that’s weak.

Alternatively, maybe it's a typo and should be 0.2, 0.4, 0.6, 0.8, 1.0, 1.2 — but it's not.

Given only three terms: 0.2, 0.6, 0.8

Difference: +0.4, +0.2 → half the increment?

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

But that’s unlikely.

Alternatively, maybe it's 0.2, 0.6, 0.8, 1.0, 1.2 — assuming from 0.8 onward, it increases by 0.2.

But why start with +0.4?

Wait — perhaps it's not arithmetic.

Another idea: Could it be fractions?

0.2 = 1/5, 0.6 = 3/5, 0.8 = 4/5 → next: 5/5 = 1.0, 6/5 = 1.2

So: 1.0, 1.2

This makes sense: numerators: 1, 3, 4, 5, 6 → not clear.

But 1, 3, 4 → maybe not.

Wait — 1/5, 3/5, 4/5, 5/5, 6/5 → yes, increasing numerator by 1 after first?

But why 1, then 3?

No.

Wait — maybe it's 0.2, 0.6, 0.8, 1.0, 1.2 — just increasing by 0.2 starting from 0.6?

But 0.2 to 0.6 is +0.4 — big jump.

Unless it's 0.2, 0.6, 0.8, 1.0, 1.2 — and the first jump is special?

But that doesn't help.

Alternatively, maybe it's 0.2, 0.6, 0.8, 1.0, 1.2 — and we accept that the pattern starts from 0.6 with +0.2.

But 0.2 to 0.6 is +0.4 — so no.

Wait — another idea: Perhaps it's 0.2, 0.6, 0.8, 1.0, 1.2 — and the pattern is: add 0.4, then add 0.2, then add 0.2, etc.

So: +0.4, +0.2, +0.2, +0.2

So next two: 0.8 + 0.2 = 1.0, 1.0 + 0.2 = 1.2

✔ Answer: 1.0, 1.2

(Though the first jump is larger, but maybe it's intentional.)

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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, ____, ____

- 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
- 5.3 → ? → +1.5 → 6.8
- Then 6.8 → 8.3 → +1.5 → yes!
- 8.3 → 9.8 → +1.5
- 9.8 → 11.3 → +1.5
- So the sequence is: +1.5 each time.

So missing:
- After 5.3: 6.8
- After 11.3: 12.8

✔ Answer: 6.8, 12.8

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✔ Final Answers:

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: +0.4, +0.2, then +0.2)*
17) 0, 1
18) 90, 99
19) 64, 125
20) 225, 256
21) 6.8, 12.8

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Let me know if you'd like an explanation for any specific one!