Grade 7 Maths Worksheet: Number patterns | Smartkids - Free Printable
Educational worksheet: Grade 7 Maths Worksheet: Number patterns | Smartkids. Download and print for classroom or home learning activities.
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Step-by-step solution for: Grade 7 Maths Worksheet: Number patterns | Smartkids
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Show Answer Key & Explanations
Step-by-step solution for: Grade 7 Maths Worksheet: Number patterns | Smartkids
Let’s go through each number pattern one by one. We’ll look at how the numbers change from one to the next — that’s called the “rule” of the pattern.
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1. 3; 6; 9; 12; ...
Each number goes up by 3.
3 + 3 = 6
6 + 3 = 9
9 + 3 = 12
So next: 12 + 3 = 15, then 15 + 3 = 18
→ Answer: 15, 18
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2. 32; 41; 51; ...
32 to 41 → +9
41 to 51 → +10
Hmm, not the same. Let’s check again.
Wait — maybe it’s increasing by 9, then 10? Then next might be +11?
51 + 11 = 62
Then 62 + 12 = 74
But let’s double-check if there’s another way.
Actually, looking again:
32 → 41 is +9
41 → 51 is +10
So yes, adding one more each time: +9, +10, +11, +12...
→ Answer: 62, 74
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3. 18; 27; 36; ...
18 to 27 → +9
27 to 36 → +9
So keep adding 9.
36 + 9 = 45
45 + 9 = 54
→ Answer: 45, 54
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4. 0,5; 0,5; 0,7; ...
First two are same: 0.5, 0.5
Then jumps to 0.7 → that’s +0.2
Maybe next is +0.2 again? 0.7 + 0.2 = 0.9
Then 0.9 + 0.2 = 1.1
But why did it stay at 0.5 twice? Maybe it’s a typo or special rule?
Looking at other patterns, this seems odd. But since only three numbers given, and last jump was +0.2, we’ll assume continues +0.2.
→ Answer: 0.9, 1.1
*(Note: In some curricula, comma is used for decimal point — so 0,5 means 0.5)*
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5. 12%; 20%; 28%; ...
12% to 20% → +8%
20% to 28% → +8%
So add 8% each time.
28% + 8% = 36%
36% + 8% = 44%
→ Answer: 36%, 44%
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6. 2,2; 2,5; 2,8; ...
2.2 to 2.5 → +0.3
2.5 to 2.8 → +0.3
So add 0.3 each time.
2.8 + 0.3 = 3.1
3.1 + 0.3 = 3.4
→ Answer: 3.1, 3.4
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7. 794; 790; 796; 802; ...
Let’s see differences:
794 → 790 = -4
790 → 796 = +6
796 → 802 = +6
Not consistent. Wait — maybe alternating?
From 794 to 790: -4
Then 790 to 796: +6
Then 796 to 802: +6 — hmm, not alternating.
Wait — perhaps after first drop, it increases by 6?
If so, next: 802 + 6 = 808
Then 808 + 6 = 814
But why start with -4? Maybe mistake? Or different rule?
Alternative idea: Look at digits?
794 → 7+9+4=20
790 → 7+9+0=16
796 → 7+9+6=22
802 → 8+0+2=10 — doesn’t help.
Back to differences: -4, +6, +6 — maybe next is +6 again?
We’ll go with that unless better idea.
→ Answer: 808, 814
*(Note: This one is tricky — but based on last two steps being +6, we continue that.)*
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8. R15; R30; R45; ...
R probably means Rand (money).
15 to 30 → +15
30 to 45 → +15
So add 15 each time.
45 + 15 = R60
60 + 15 = R75
→ Answer: R60, R75
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9. 16; 25; 36; 49; ...
These are perfect squares!
4² = 16
5² = 25
6² = 36
7² = 49
Next: 8² = 64
Then 9² = 81
→ Answer: 64, 81
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10. ½; ¾; 1; ...
Convert to decimals or common denominator.
½ = 0.5
¾ = 0.75
1 = 1.00
Difference: 0.75 - 0.5 = 0.25
1.00 - 0.75 = 0.25
So add 0.25 each time.
1.00 + 0.25 = 1.25 → which is 5/4 or 1¼
1.25 + 0.25 = 1.50 → which is 3/2 or 1½
In fractions:
After 1 (which is 4/4), next is 5/4, then 6/4 = 3/2
→ Answer: 5/4, 3/2 (or 1¼, 1½)
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11. 945; 925; 905; ...
945 to 925 → -20
925 to 905 → -20
So subtract 20 each time.
905 - 20 = 885
885 - 20 = 865
→ Answer: 885, 865
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12. 1,6; 1,6; 1,3; ...
1.6, 1.6 → same
Then 1.6 to 1.3 → -0.3
Maybe next is -0.3 again? 1.3 - 0.3 = 1.0
Then 1.0 - 0.3 = 0.7
Why repeat first? Maybe error or special case — but following last change.
→ Answer: 1.0, 0.7
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13. 84; 72; 60; ...
84 to 72 → -12
72 to 60 → -12
Subtract 12 each time.
60 - 12 = 48
48 - 12 = 36
→ Answer: 48, 36
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14. -4; -2; -2; -1; 0; ...
Let’s list them:
-4 → -2 → -2 → -1 → 0
Differences:
-4 to -2: +2
-2 to -2: +0
-2 to -1: +1
-1 to 0: +1
Not clear. Maybe group?
Or think: after -4, it goes to -2 (up 2), stays at -2, then up 1 to -1, up 1 to 0.
Maybe next: up 1 again? 0 + 1 = 1
Then 1 + 1 = 2
But why the +2 at start? Perhaps irregular.
Another idea: maybe it’s counting up slowly after stabilizing.
Since last two steps were +1, continue +1.
→ Answer: 1, 2
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15. 3; 9; 27; 81; ...
3 × 3 = 9
9 × 3 = 27
27 × 3 = 81
Multiply by 3 each time.
81 × 3 = 243
243 × 3 = 729
→ Answer: 243, 729
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Final Answer:
1. 15, 18
2. 62, 74
3. 45, 54
4. 0.9, 1.1
5. 36%, 44%
6. 3.1, 3.4
7. 808, 814
8. R60, R75
9. 64, 81
10. 5/4, 3/2 (or 1¼, 1½)
11. 885, 865
12. 1.0, 0.7
13. 48, 36
14. 1, 2
15. 243, 729
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1. 3; 6; 9; 12; ...
Each number goes up by 3.
3 + 3 = 6
6 + 3 = 9
9 + 3 = 12
So next: 12 + 3 = 15, then 15 + 3 = 18
→ Answer: 15, 18
---
2. 32; 41; 51; ...
32 to 41 → +9
41 to 51 → +10
Hmm, not the same. Let’s check again.
Wait — maybe it’s increasing by 9, then 10? Then next might be +11?
51 + 11 = 62
Then 62 + 12 = 74
But let’s double-check if there’s another way.
Actually, looking again:
32 → 41 is +9
41 → 51 is +10
So yes, adding one more each time: +9, +10, +11, +12...
→ Answer: 62, 74
---
3. 18; 27; 36; ...
18 to 27 → +9
27 to 36 → +9
So keep adding 9.
36 + 9 = 45
45 + 9 = 54
→ Answer: 45, 54
---
4. 0,5; 0,5; 0,7; ...
First two are same: 0.5, 0.5
Then jumps to 0.7 → that’s +0.2
Maybe next is +0.2 again? 0.7 + 0.2 = 0.9
Then 0.9 + 0.2 = 1.1
But why did it stay at 0.5 twice? Maybe it’s a typo or special rule?
Looking at other patterns, this seems odd. But since only three numbers given, and last jump was +0.2, we’ll assume continues +0.2.
→ Answer: 0.9, 1.1
*(Note: In some curricula, comma is used for decimal point — so 0,5 means 0.5)*
---
5. 12%; 20%; 28%; ...
12% to 20% → +8%
20% to 28% → +8%
So add 8% each time.
28% + 8% = 36%
36% + 8% = 44%
→ Answer: 36%, 44%
---
6. 2,2; 2,5; 2,8; ...
2.2 to 2.5 → +0.3
2.5 to 2.8 → +0.3
So add 0.3 each time.
2.8 + 0.3 = 3.1
3.1 + 0.3 = 3.4
→ Answer: 3.1, 3.4
---
7. 794; 790; 796; 802; ...
Let’s see differences:
794 → 790 = -4
790 → 796 = +6
796 → 802 = +6
Not consistent. Wait — maybe alternating?
From 794 to 790: -4
Then 790 to 796: +6
Then 796 to 802: +6 — hmm, not alternating.
Wait — perhaps after first drop, it increases by 6?
If so, next: 802 + 6 = 808
Then 808 + 6 = 814
But why start with -4? Maybe mistake? Or different rule?
Alternative idea: Look at digits?
794 → 7+9+4=20
790 → 7+9+0=16
796 → 7+9+6=22
802 → 8+0+2=10 — doesn’t help.
Back to differences: -4, +6, +6 — maybe next is +6 again?
We’ll go with that unless better idea.
→ Answer: 808, 814
*(Note: This one is tricky — but based on last two steps being +6, we continue that.)*
---
8. R15; R30; R45; ...
R probably means Rand (money).
15 to 30 → +15
30 to 45 → +15
So add 15 each time.
45 + 15 = R60
60 + 15 = R75
→ Answer: R60, R75
---
9. 16; 25; 36; 49; ...
These are perfect squares!
4² = 16
5² = 25
6² = 36
7² = 49
Next: 8² = 64
Then 9² = 81
→ Answer: 64, 81
---
10. ½; ¾; 1; ...
Convert to decimals or common denominator.
½ = 0.5
¾ = 0.75
1 = 1.00
Difference: 0.75 - 0.5 = 0.25
1.00 - 0.75 = 0.25
So add 0.25 each time.
1.00 + 0.25 = 1.25 → which is 5/4 or 1¼
1.25 + 0.25 = 1.50 → which is 3/2 or 1½
In fractions:
After 1 (which is 4/4), next is 5/4, then 6/4 = 3/2
→ Answer: 5/4, 3/2 (or 1¼, 1½)
---
11. 945; 925; 905; ...
945 to 925 → -20
925 to 905 → -20
So subtract 20 each time.
905 - 20 = 885
885 - 20 = 865
→ Answer: 885, 865
---
12. 1,6; 1,6; 1,3; ...
1.6, 1.6 → same
Then 1.6 to 1.3 → -0.3
Maybe next is -0.3 again? 1.3 - 0.3 = 1.0
Then 1.0 - 0.3 = 0.7
Why repeat first? Maybe error or special case — but following last change.
→ Answer: 1.0, 0.7
---
13. 84; 72; 60; ...
84 to 72 → -12
72 to 60 → -12
Subtract 12 each time.
60 - 12 = 48
48 - 12 = 36
→ Answer: 48, 36
---
14. -4; -2; -2; -1; 0; ...
Let’s list them:
-4 → -2 → -2 → -1 → 0
Differences:
-4 to -2: +2
-2 to -2: +0
-2 to -1: +1
-1 to 0: +1
Not clear. Maybe group?
Or think: after -4, it goes to -2 (up 2), stays at -2, then up 1 to -1, up 1 to 0.
Maybe next: up 1 again? 0 + 1 = 1
Then 1 + 1 = 2
But why the +2 at start? Perhaps irregular.
Another idea: maybe it’s counting up slowly after stabilizing.
Since last two steps were +1, continue +1.
→ Answer: 1, 2
---
15. 3; 9; 27; 81; ...
3 × 3 = 9
9 × 3 = 27
27 × 3 = 81
Multiply by 3 each time.
81 × 3 = 243
243 × 3 = 729
→ Answer: 243, 729
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Final Answer:
1. 15, 18
2. 62, 74
3. 45, 54
4. 0.9, 1.1
5. 36%, 44%
6. 3.1, 3.4
7. 808, 814
8. R60, R75
9. 64, 81
10. 5/4, 3/2 (or 1¼, 1½)
11. 885, 865
12. 1.0, 0.7
13. 48, 36
14. 1, 2
15. 243, 729
Parent Tip: Review the logic above to help your child master the concept of pattern and equations worksheet.
