Let's solve each pattern step by step and explain the reasoning behind each.
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1. 35, ____, 55, 65, 75, 85, 95
- Look at the numbers:
35 → ? → 55 → 65 → 75 → 85 → 95
- The difference between consecutive terms:
- 55 – 35 = 20 → so if there’s one missing number, it should be halfway?
- But wait: from 55 to 65 is +10, 65 to 75 is +10, etc.
- So after 35, the next number must be such that:
- From 35 to next: ?
- Then to 55: +20?
But let's check:
If we go from 35 to 55 = +20, then the missing number is
45, because:
- 35 → 45 (+10)
- 45 → 55 (+10)
- 55 → 65 (+10), etc.
So this is an arithmetic sequence increasing by
10.
✔ Answer: 45
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2. 10, 25, 40, ____, 70, 85
- Differences:
- 25 – 10 = 15
- 40 – 25 = 15
- So pattern increases by 15
- Next: 40 + 15 =
55
- Check: 55 + 15 = 70
✔
- 70 + 15 = 85
✔
✔ Answer: 55
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3. 25, ____, 75, 100
- From 25 to 75 = +50
- From 75 to 100 = +25
But the increase is not constant. Let's look at possible pattern.
Try: 25 → ? → 75 → 100
Could it be increasing by multiples?
Check differences:
- If we assume a linear pattern with two steps:
- From 25 to 75 = +50 over 2 steps → average +25 per step
- So maybe: 25 → 50 → 75 → 100
Check:
- 25 → 50 (+25)
- 50 → 75 (+25)
- 75 → 100 (+25)
Yes! It's increasing by
25 each time.
✔ Answer: 50
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4. 7, 14, 21, ____, 35, 42, 49
- Differences:
- 14 – 7 = 7
- 21 – 14 = 7
- So pattern: +7 each time
- 21 + 7 =
28
- 28 + 7 = 35
✔
- 35 + 7 = 42
✔
✔ Answer: 28
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5. 100, 90, 80, ____, 60, 50, 40
- Decreasing by 10 each time:
- 100 → 90 (–10)
- 90 → 80 (–10)
- 80 → ? → should be 70
- 70 → 60 (–10), etc.
✔ Answer: 70
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6. 1, 3, 6, 10, ____, 21, 28, 36
- This looks familiar: triangular numbers!
Check:
- 1 → 3 (diff: +2)
- 3 → 6 (+3)
- 6 → 10 (+4)
- So next: +5 → 10 + 5 =
15
- Then +6 → 15 + 6 = 21
✔
- +7 → 28
✔
- +8 → 36
✔
Pattern: adding consecutive integers starting from 2.
✔ Answer: 15
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7. 23, 26, ____, 32, 35, 38
- 23 → 26 = +3
- 26 → ? → 32
- 32 → 35 = +3
- 35 → 38 = +3
So likely increasing by
+3 each time.
- 26 + 3 =
29
- 29 + 3 = 32
✔
✔ Answer: 29
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8. 24, 20, 16, ____, 8, 4
- Decreasing by 4:
- 24 → 20 (–4)
- 20 → 16 (–4)
- 16 → ? → should be
12
- 12 → 8 (–4)
- 8 → 4 (–4)
✔ Answer: 12
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9. 2, 4, 6, ____, 10, 12, 14
- Even numbers increasing by 2:
- 2 → 4 → 6 → ? → 10 → 12 → 14
- 6 + 2 =
8
✔ Answer: 8
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10. 8, 16, 24, 32, ____, 48, 56
- Increasing by 8:
- 8 → 16 (+8)
- 16 → 24 (+8)
- 24 → 32 (+8)
- 32 → ? → should be
40
- 40 → 48 (+8)
- 48 → 56 (+8)
✔ Answer: 40
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✔ Final Answers:
1.
45
2.
55
3.
50
4.
28
5.
70
6.
15
7.
29
8.
12
9.
8
10.
40
Let me know if you'd like these explained in a table or visual format!
Parent Tip: Review the logic above to help your child master the concept of sequences worksheet year 5.
