Counting on by digits worksheet for practicing number sequences with missing numbers.

Let's solve each sequence step by step. The key instruction is: "Each of these sequences goes up by single digit steps." This means the numbers increase by a constant amount (a single-digit number, like 1, 2, 3, etc.).

We'll determine the pattern (common difference) and fill in the missing numbers.

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1)

Sequence: ` _, 7, 14, _, 28, _, 42, _`

- From 7 to 14: +7 → So the step is +7
- Let’s fill in:
- Before 7: 7 – 7 = 0
- After 14: 14 + 7 = 21
- After 28: 28 + 7 = 35
- After 42: 42 + 7 = 49

✔ Sequence: 0, 7, 14, 21, 28, 35, 42, 49

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2)

Sequence: `0, _, 8, 12, _, 20, _, _`

- From 0 to 8: +8? But then 8 to 12 is +4 → Not consistent.
Wait — let's check differences:
- Between 8 and 12: +4
- Between 12 and 20: +8 → not consistent.

Wait — maybe we need to find a common step.

Try checking possible patterns:

But wait — it says "single digit steps", so the increment should be constant, and a single digit (1–9).

Let’s try to see what step fits.

From 0 to 8: could be +4? Then:
- 0, 4, 8, 12, 16, 20, 24, 28

Check if that works:
- 0, ?, 8, 12, ?, 20, ?, ?

So:
- 0, 4, 8, 12, 16, 20, 24, 28

Yes! Step = +4

Fill in:
- First blank: 0 + 4 = 4
- After 12: 12 + 4 = 16
- After 20: 20 + 4 = 24
- Last: 24 + 4 = 28

✔ Sequence: 0, 4, 8, 12, 16, 20, 24, 28

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3)

Sequence: `8, _, 12, _, 16, 18, _, _`

Look at known values:
- 8 to 12 = +4 → maybe step is +2?

Try step = +2:
- 8, 10, 12, 14, 16, 18, 20, 22

Yes! That matches:
- 8, [10], 12, [14], 16, 18, [20], [22]

✔ Sequence: 8, 10, 12, 14, 16, 18, 20, 22

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4)

Sequence: `12, 15, _, 21, _, _, _, 30, _`

- 12 to 15 = +3 → likely step = +3
- Check: 15 + 3 = 18 → next
- 18 + 3 = 21 → yes!
- 21 + 3 = 24
- 24 + 3 = 27
- 27 + 3 = 30 → yes!
- 30 + 3 = 33

Now fill in:
- After 15: 18
- After 21: 24, 27
- After 30: 33

✔ Sequence: 12, 15, 18, 21, 24, 27, 30, 33

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5)

Sequence: `0, _, 18, 27, _, _, _, 54, _`

- 0 to 18 = +18 → too big. But step must be single digit.
- Try from 18 to 27: +9 → so maybe step = +9?
- Check: 0, 9, 18, 27, 36, 45, 54, 63

Yes! All steps are +9 → single digit step.

So:
- After 0: 9
- After 27: 36, 45
- After 54: 63

✔ Sequence: 0, 9, 18, 27, 36, 45, 54, 63

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6)

Sequence: `_, 17, 22, _, 32, _, 42, _`

- 17 to 22 = +5 → step = +5?
- Then before 17: 17 – 5 = 12
- After 22: 22 + 5 = 27
- After 32: 32 + 5 = 37
- After 42: 42 + 5 = 47

Check:
- 12, 17, 22, 27, 32, 37, 42, 47 → all +5 → valid

✔ Sequence: 12, 17, 22, 27, 32, 37, 42, 47

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7)

Sequence: `_, 12, _, 24, _, 36, 42, _`

Look at knowns:
- 12, 24, 36, 42

But 12 to 24 = +12 → too big. Wait — but 36 to 42 = +6 → maybe step is +6?

Try step = +6:
- 12, 18, 24, 30, 36, 42, 48

But we have:
- _, 12, _, 24, _, 36, 42, _

So positions:
- Pos 1: ?
- Pos 2: 12
- Pos 3: ?
- Pos 4: 24
- Pos 5: ?
- Pos 6: 36
- Pos 7: 42
- Pos 8: ?

If step = +6:
- 12 – 6 = 6 → first number
- 12 + 6 = 18
- 24 + 6 = 30
- 36 + 6 = 42 → already there
- 42 + 6 = 48

So:
- 6, 12, 18, 24, 30, 36, 42, 48

✔ Sequence: 6, 12, 18, 24, 30, 36, 42, 48

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8)

Sequence: `19, _, 23, _, 27, 29, _, _`

Look at knowns:
- 19, ?, 23, ?, 27, 29, ?, ?

Try step = +2?
- 19, 21, 23, 25, 27, 29, 31, 33 → yes!

Check:
- 19 → 21 → 23 → 25 → 27 → 29 → 31 → 33

Perfect.

So blanks:
- After 19: 21
- After 23: 25
- After 29: 31, 33

✔ Sequence: 19, 21, 23, 25, 27, 29, 31, 33

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9)

Sequence: `_, 24, 32, _, 48, _, _, 64, _`

- 24 to 32 = +8 → step = +8?
- Then before 24: 24 – 8 = 16
- After 32: 32 + 8 = 40
- After 48: 48 + 8 = 56
- Next: 56 + 8 = 64 → matches
- After 64: 64 + 8 = 72

So:
- 16, 24, 32, 40, 48, 56, 64, 72

✔ Sequence: 16, 24, 32, 40, 48, 56, 64, 72

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10)

Sequence: `17, _, _, 20, 21, _, _, _, 24`

Known: 17, ?, ?, 20, 21, ?, ?, ?, 24

Look at 20 → 21 = +1 → maybe step = +1?

Then:
- 17, 18, 19, 20, 21, 22, 23, 24

That fits perfectly.

So:
- After 17: 18, 19
- After 21: 22, 23
- After 23: 24

✔ Sequence: 17, 18, 19, 20, 21, 22, 23, 24

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✔ Final Answers:

1) 0, 7, 14, 21, 28, 35, 42, 49
2) 0, 4, 8, 12, 16, 20, 24, 28
3) 8, 10, 12, 14, 16, 18, 20, 22
4) 12, 15, 18, 21, 24, 27, 30, 33
5) 0, 9, 18, 27, 36, 45, 54, 63
6) 12, 17, 22, 27, 32, 37, 42, 47
7) 6, 12, 18, 24, 30, 36, 42, 48
8) 19, 21, 23, 25, 27, 29, 31, 33
9) 16, 24, 32, 40, 48, 56, 64, 72
10) 17, 18, 19, 20, 21, 22, 23, 24

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All sequences follow a constant single-digit increment, as required. Each step is between 1 and 9, and the pattern is consistent across all sequences.

Let me know if you'd like this formatted for printing or with explanations per row!