Grade 5 math fun & engaging number patterns and sequences worksheets - Free Printable

Let's solve each sequence step by step and determine the missing number, then choose the correct answer from the options provided.

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a. 2, 12, 72, ____, 2,592, 15,552

Let’s look at the pattern:

- 2 → 12:
$ 2 \times 6 = 12 $
- 12 → 72:
$ 12 \times 6 = 72 $
- 72 → ? :
$ 72 \times 6 = 432 $
- 432 → 2,592:
$ 432 \times 6 = 2,592 $
- 2,592 → 15,552:
$ 2,592 \times 6 = 15,552 $

✔ So the pattern is multiply by 6.

Missing number = $ 72 \times 6 = 432 $

Now check the options:
- □ 432 ✔
- □ 84
- □ 254
- □ 48

👉 Answer: 432

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b. 2, 4, 6, 8, 10, 12

This is an arithmetic sequence increasing by 2.

All numbers are even, going up by 2.

So the next number after 12 would be 14, but we're being asked to fill in a missing number — but all numbers are present.

Wait — actually, the sequence is complete: 2, 4, 6, 8, 10, 12.

But there’s a blank: “____” after 10?

Wait — let's re-read:
"2, 4, 6, 8, 10, 12, ____"

So it's asking for the next number.

But the pattern is +2 each time.

So:
12 + 2 = 14

Now check options:
- □ 16
- □ 18
- □ 14 ✔
- □ 15

👉 Answer: 14

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c. 6, 10, 14, ____, 22

Check differences:
- 10 - 6 = 4
- 14 - 10 = 4
- So next: 14 + 4 = 18
- Then 18 + 4 = 22 → matches!

So missing number = 18

Options:
- □ 16
- □ 17
- □ 19
- □ 18 ✔

👉 Answer: 18

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d. 23, 18, 13, 8, ____

Look at the pattern:
- 23 → 18: −5
- 18 → 13: −5
- 13 → 8: −5
- 8 → ? : −5 → 3

So missing number = 3

Options:
- □ 3 ✔
- □ 4
- □ 5
- □ 6

👉 Answer: 3

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e. 1, 10, ____, 46, 64, 82

Let’s look at the differences between known terms:

- 10 - 1 = 9
- 46 - ? = ?
- 64 - 46 = 18
- 82 - 64 = 18

So from 46 onward, the difference is +18.

But before that, from 10 to ?, then to 46.

Assume constant difference? Let’s see:

Try to find a pattern.

Let’s suppose the sequence increases by +18 every two steps?

Alternatively, maybe the difference increases.

Try:

- 1 → 10: +9
- 10 → ? : let’s say +x
- ? → 46: +y
- 46 → 64: +18
- 64 → 82: +18

So last two steps: +18, +18 → consistent.

What about earlier?

Maybe the pattern is increasing by +9, then +18, etc.? But not clear.

Try assuming the sequence has a common difference of 18 starting from some point.

Wait — let’s try to find what comes after 10.

Suppose the sequence increases by +18 every step? Then:

- 1 → 19 → 37 → 55 → 73 → 91 → no, doesn’t match.

Wait — let’s try this:

List: 1, 10, ?, 46, 64, 82

Let’s compute the differences:

- 10 - 1 = 9
- ? - 10 = ?
- 46 - ? = ?
- 64 - 46 = 18
- 82 - 64 = 18

So from 46 onward, it's +18.

So perhaps the sequence increases by +9, then +18, then +18, etc.? Not likely.

Wait — maybe the second difference is constant?

Try assuming the missing term is 28 (one of the options).

Try: 1, 10, 28, 46, 64, 82

Check differences:
- 10 - 1 = 9
- 28 - 10 = 18
- 46 - 28 = 18
- 64 - 46 = 18
- 82 - 64 = 18

So: +9, then +18, +18, +18, +18

That’s possible — maybe it starts with +9, then continues with +18.

But why?

Alternatively, maybe it’s quadratic?

Another idea: Could it be multiples of something?

Wait — look at the numbers: 1, 10, ?, 46, 64, 82

Notice:

- 1 = 1×1
- 10 = 2×5
- 46 = 2×23
- 64 = 8×8
- 82 = 2×41

Not helpful.

Wait — look at differences between consecutive terms:

We have:

- 1 → 10: +9
- 10 → ? : let’s call it x
- ? → 46: y
- 46 → 64: +18
- 64 → 82: +18

If the last three differences are +18, maybe the one before that is also +18?

So:
? → 46 = +18 → so ? = 46 - 18 = 28

Then: 10 → 28 = +18

But earlier: 1 → 10 = +9

So: +9, +18, +18, +18, +18

That works — maybe the first increase is +9, then it becomes +18.

So missing number = 28

Now check options:
- □ 28 ✔
- □ 27
- □ 18
- □ 36

👉 Answer: 28

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f. 1, 4, 8, 12, 16, 20, ____

Sequence: 1, 4, 8, 12, 16, 20

Differences:
- 4 - 1 = 3
- 8 - 4 = 4
- 12 - 8 = 4
- 16 - 12 = 4
- 20 - 16 = 4

So: +3, then +4, +4, +4, +4 → so likely next is +4 → 20 + 4 = 24

But wait — first jump is +3, then +4 repeatedly.

So next = 24

Now check options:
- □ 34
- □ 48
- □ 32
- □ 24 ✔

👉 Answer: 24

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g. 0, 6, 18, ____, 27, 34, 41

Wait — this seems odd.

Sequence: 0, 6, 18, ____, 27, 34, 41

But look: after 18, the next known term is 27, then 34, 41.

But 27 is less than 18? No — 27 > 18, okay.

Wait: 0, 6, 18, ?, 27, 34, 41

Check differences:

- 6 - 0 = 6
- 18 - 6 = 12
- ? - 18 = ?
- 27 - ? = ?
- 34 - 27 = 7
- 41 - 34 = 7

So from 27 onward: +7, +7 → arithmetic.

But before that: 0 → 6 (+6), 6 → 18 (+12)

So maybe doubling the increment?

Next could be +18? Then 18 + 18 = 36

Then 36 → 27? That would be −9, which breaks the pattern.

But then 27 → 34 → +7

No.

Wait — maybe the sequence is not continuous?

Wait — could the sequence be split?

Or maybe the missing number is 24, and then 27?

But 18 → 24 = +6, 24 → 27 = +3 → not consistent.

Wait — another idea: maybe the sequence is based on positions?

Let’s list:

- Term 1: 0
- Term 2: 6
- Term 3: 18
- Term 4: ?
- Term 5: 27
- Term 6: 34
- Term 7: 41

From term 5 onward: 27, 34, 41 → +7, +7 → so arithmetic with difference 7.

So term 5 = 27, term 6 = 34, term 7 = 41

Now term 4 must be such that the pattern makes sense.

But term 3 = 18, term 4 = ?, term 5 = 27

So ? → 27 = ?

If we assume +9, then ? = 18 → 27 = +9 → so ? = 18 → 27 → so ? = 18 + 9 = 27? But 27 is already term 5.

Wait — if term 4 = x, then x → 27 = ?

And 27 → 34 = +7, so previous difference might be different.

But maybe the increase is changing.

Try to see if it's quadratic or based on multiples.

Wait — another thought: maybe the sequence is:

0, 6, 18, 24, 27, 34, 41?

But 18 → 24 = +6, 24 → 27 = +3 → not good.

Wait — maybe it's two interleaved sequences?

Odd positions: 1st, 3rd, 5th, 7th: 0, 18, 27, 41

Even positions: 2nd, 4th, 6th: 6, ?, 34

Let’s try:

Odd positions:
- 1: 0
- 3: 18
- 5: 27
- 7: 41

Differences:
- 18 - 0 = 18
- 27 - 18 = 9
- 41 - 27 = 14 → no clear pattern

Even positions:
- 2: 6
- 4: ?
- 6: 34

So 6 → ? → 34

If linear: average increase: (34 - 6)/2 = 14 → so ? = 6 + 14 = 20

Then 20 → 34 = +14

So ? = 20

Now check: 6, 20, 34 → +14, +14 → yes.

So missing number (even position) = 20

Now check options:
- □ 20 ✔
- □ 24
- □ 26
- □ 28

So 20 is an option.

Now verify if this fits overall.

Sequence:
1: 0
2: 6
3: 18
4: 20
5: 27
6: 34
7: 41

Now check if this makes sense.

From 18 (term 3) to 20 (term 4): +2
Then 20 to 27: +7
Then 27 to 34: +7
Then 34 to 41: +7

So after term 4, it goes +7, +7, +7

But before: 0→6 (+6), 6→18 (+12), 18→20 (+2), 20→27 (+7)

Not very clean.

But maybe the rule is from term 5 onward: add 7.

Term 4 is 20, then 27 → +7 → okay.

Is there a better fit?

Try 24 as missing number.

Then: 18 → 24 = +6, 24 → 27 = +3 → not consistent.

Try 26: 18→26=+8, 26→27=+1 → no.

Try 28: 18→28=+10, 28→27=−1 → no.

Only 20 gives 20→27=+7, matching later pattern.

So even though the earlier parts are messy, 20 is the only value that makes the last three terms follow a clear +7 pattern.

Moreover, the even-positioned terms: 6, ?, 34

If we assume arithmetic: 6, x, 34 → then x = (6 + 34)/2 = 20 → yes!

So 20 is the midpoint.

So missing number = 20

✔ Answer: 20

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✔ Final Answers:

| Letter | Sequence | Missing Number | Correct Option |
|--------|----------|----------------|----------------|
| a | 2, 12, 72, __, 2592, 15552 | 432 | □ 432 ✔ |
| b | 2, 4, 6, 8, 10, 12, ____ | 14 | □ 14 ✔ |
| c | 6, 10, 14, __, 22 | 18 | □ 18 ✔ |
| d | 23, 18, 13, 8, ____ | 3 | □ 3 ✔ |
| e | 1, 10, __, 46, 64, 82 | 28 | □ 28 ✔ |
| f | 1, 4, 8, 12, 16, 20, ____ | 24 | □ 24 ✔ |
| g | 0, 6, 18, __, 27, 34, 41 | 20 | □ 20 ✔ |

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📌 Summary of Rules:

- a: Multiply by 6
- b: Add 2
- c: Add 4
- d: Subtract 5
- e: After 10, add 18 each time
- f: First +3, then +4 repeatedly
- g: Even-positioned terms form arithmetic sequence: 6, 20, 34 (add 14)

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✔ All answers are filled correctly!