Let's solve each pattern step by step and explain the reasoning behind each.
---
1. 2, 4, 6, 8, __, 12
- Pattern: Increasing by 2 each time.
- 2 → 4 (+2)
- 4 → 6 (+2)
- 6 → 8 (+2)
- 8 → ? → 12
- So, 8 + 2 =
10, then 10 + 2 = 12
✔
✔ Answer: 10
---
2. 3, 5, 7, __, __, 13
- Pattern: Increasing by 2 each time (odd numbers).
- 3 → 5 (+2)
- 5 → 7 (+2)
- 7 → ? → ? → 13
- Next: 7 + 2 =
9
- Then: 9 + 2 =
11
- Then: 11 + 2 = 13
✔
✔ Answer: 9, 11
---
3. 8, 11, __, 17, 20, __
- Pattern: Check differences:
- 8 → 11: +3
- 11 → ? → 17 → 20 → ?
- So likely adding 3 each time:
- 11 + 3 =
14
- 14 + 3 = 17
✔
- 17 + 3 = 20
✔
- 20 + 3 =
23
✔ Answer: 14, 23
---
4. 18, 15, __, __, 6, 3
- Pattern: Decreasing.
- 18 → 15: −3
- 15 → ? → ? → 6 → 3
- So subtracting 3 each time:
- 15 − 3 =
12
- 12 − 3 =
9
- 9 − 3 = 6
✔
- 6 − 3 = 3
✔
✔ Answer: 12, 9
---
5. 75, 72, __, __, 63, 60
- Pattern: Decreasing.
- 75 → 72: −3
- So next: 72 − 3 =
69
- 69 − 3 =
66
- 66 − 3 = 63
✔
- 63 − 3 = 60
✔
✔ Answer: 69, 66
---
6. 88, 77, 66, __, __, 33
- Pattern: Decreasing by 11 each time?
- 88 → 77: −11
- 77 → 66: −11
- 66 → ? → ? → 33
- So:
- 66 − 11 =
55
- 55 − 11 =
44
- 44 − 11 = 33
✔
✔ Answer: 55, 44
---
7. 9, 13, 9, __, 9, 13
- Alternating pattern: 9, 13, 9, ?, 9, 13
- Positions:
- 1st: 9
- 2nd: 13
- 3rd: 9
- 4th: ?
- 5th: 9
- 6th: 13
- So it alternates between 9 and 13.
- Odd positions: 9, 9, 9 → always 9
- Even positions: 13, ?, 13 → so missing is
13
✔ Answer: 13
---
8. 17, 18, 6, __, 18, 6
- Pattern: Let’s look at groups:
- 17, 18, 6
- ?, 18, 6
- Maybe repeating pattern? Look at positions:
- 1: 17
- 2: 18
- 3: 6
- 4: ?
- 5: 18
- 6: 6
Wait — notice that from position 2 to 3: 18 → 6
Then from 5 to 6: 18 → 6 → same
But what about position 4?
Maybe a repeating cycle of
17, 18, 6?
But first three: 17, 18, 6
Next: 17, 18, 6 → but we have:
Position 4: ?
Position 5: 18
Position 6: 6
So if it's repeating every 3:
- Group 1: 17, 18, 6
- Group 2: ?, 18, 6 → so missing number should be
17
Yes! Because:
- Position 1: 17
- Position 2: 18
- Position 3: 6
- Position 4: 17 (start of new cycle)
- Position 5: 18
- Position 6: 6
✔ Answer: 17
---
✔ Final Answers:
1.
10
2.
9, 11
3.
14, 23
4.
12, 9
5.
69, 66
6.
55, 44
7.
13
8.
17
Let me know if you'd like this printed or formatted for a worksheet!
Parent Tip: Review the logic above to help your child master the concept of math pattern worksheet.
