Let's solve each of these number pattern questions step by step and explain the reasoning.
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Question 1:
Pattern: 2, 5, 8, 11, ...
Look at the differences between consecutive numbers:
- 5 - 2 = 3
- 8 - 5 = 3
- 11 - 8 = 3
This is an
arithmetic sequence with a common difference of
+3.
So:
- Next number: 11 + 3 =
14
- After that: 14 + 3 =
17
✔ Answer:
A) 14, 17
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Question 2:
Pattern: 2, 6, 10, 14, ...
Differences:
- 6 - 2 = 4
- 10 - 6 = 4
- 14 - 10 = 4
Common difference:
+4
Next:
- 14 + 4 =
18
- 18 + 4 =
22
✔ Answer:
C) 18, 22
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Question 3:
Pattern: 2, 7, 12, 17, ...
Differences:
- 7 - 2 = 5
- 12 - 7 = 5
- 17 - 12 = 5
Common difference:
+5
Next:
- 17 + 5 =
22
- 22 + 5 =
27
✔ Answer:
B) 22, 27
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Question 4:
Pattern: 3, 7, 11, 15, ...
Differences:
- 7 - 3 = 4
- 11 - 7 = 4
- 15 - 11 = 4
Common difference:
+4
Next:
- 15 + 4 =
19
- 19 + 4 =
23
✔ Answer:
C) 19, 23
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Question 5:
Pattern: 3, 8, 13, 18, ...
Differences:
- 8 - 3 = 5
- 13 - 8 = 5
- 18 - 13 = 5
Common difference:
+5
Next:
- 18 + 5 =
23
- 23 + 5 =
28
✔ Answer:
C) 23, 28
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Question 6:
Pattern: 3, 9, 15, 21, ...
Differences:
- 9 - 3 = 6
- 15 - 9 = 6
- 21 - 15 = 6
Common difference:
+6
Next:
- 21 + 6 =
27
- 27 + 6 =
33
But wait — the options aren't shown in your image. However, based on the pattern, the next two numbers are
27, 33.
If the options were:
A) 27, 33
B) 27, 32
C) 26, 32
D) 28, 34
Then correct answer would be
A) 27, 33
But since you only showed up to question 6, and no options for Q6, I’ll assume it’s similar format.
✔ Answer:
27, 33
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✔ Final Answers:
1.
A) 14, 17
2.
C) 18, 22
3.
B) 22, 27
4.
C) 19, 23
5.
C) 23, 28
6.
(Likely A) 27, 33 (if options include this)
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🔍 Pattern Summary:
All these patterns are
arithmetic sequences, meaning they increase by a constant amount:
- Add 3 → Q1
- Add 4 → Q2
- Add 5 → Q3
- Add 4 → Q4
- Add 5 → Q5
- Add 6 → Q6
To find the next numbers, just keep adding the common difference.
Let me know if you'd like help with the remaining questions (7–10)!
Parent Tip: Review the logic above to help your child master the concept of 5th grade number patterns worksheet.
