Number Patterns and Sequences worksheet with exercises for identifying and continuing numerical sequences.
A worksheet titled "Number Patterns and Sequences" with three exercises asking students to complete number sequences by filling in the next three numbers.
JPG
1000×1291
75.8 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #763333
⭐
Show Answer Key & Explanations
Step-by-step solution for: Number Patterns & Sequences worksheet
▼
Show Answer Key & Explanations
Step-by-step solution for: Number Patterns & Sequences worksheet
Let’s solve each sequence step by step. We’ll look for the pattern in each one — whether it’s adding, multiplying, subtracting, or alternating operations.
---
EXERCISE 1
(a) 2, 4, 8, 16, ___, ___, ___
Each number is multiplied by 2:
- 2 × 2 = 4
- 4 × 2 = 8
- 8 × 2 = 16
- 16 × 2 = 32
- 32 × 2 = 64
- 64 × 2 = 128
→ Next three: 32, 64, 128
---
(b) 1, 4, 7, 10, ___, ___, ___
Each number increases by 3:
- 1 + 3 = 4
- 4 + 3 = 7
- 7 + 3 = 10
- 10 + 3 = 13
- 13 + 3 = 16
- 16 + 3 = 19
→ Next three: 13, 16, 19
---
(c) 7, 14, 21, 28, ___, ___, ___
Multiples of 7:
- 7×1=7, 7×2=14, 7×3=21, 7×4=28
- 7×5 = 35
- 7×6 = 42
- 7×7 = 49
→ Next three: 35, 42, 49
---
(d) 2, 20, 200, 2000, ___, ___, ___
Each number is multiplied by 10:
- 2 × 10 = 20
- 20 × 10 = 200
- 200 × 10 = 2000
- 2000 × 10 = 20000
- 20000 × 10 = 200000
- 200000 × 10 = 2000000
→ Next three: 20000, 200000, 2000000
---
(e) 6, 12, 18, 24, ___, ___, ___
Multiples of 6:
- 6×1=6, 6×2=12, 6×3=18, 6×4=24
- 6×5 = 30
- 6×6 = 36
- 6×7 = 42
→ Next three: 30, 36, 42
---
EXERCISE 2
(a) 58, 68, 63, 73, 68, ___, ___, ___
Look at the pattern:
+10, -5, +10, -5, ...
So:
- 58 +10 = 68
- 68 -5 = 63
- 63 +10 = 73
- 73 -5 = 68
- 68 +10 = 78
- 78 -5 = 73
- 73 +10 = 83
→ Next three: 78, 73, 83
---
(b) 7, 8, 15, 23, 38, ___, ___, ___
This looks like Fibonacci-style: add previous two numbers.
Check:
- 7 + 8 = 15 ✔
- 8 + 15 = 23 ✔
- 15 + 23 = 38 ✔
- 23 + 38 = 61
- 38 + 61 = 99
- 61 + 99 = 160
→ Next three: 61, 99, 160
---
(c) 55, 34, 21, 13, 8, ___, ___, ___
Subtracting: each number is the difference of the two before? Or going down?
Actually, this is reverse Fibonacci:
55 - 34 = 21
34 - 21 = 13
21 - 13 = 8
13 - 8 = 5
8 - 5 = 3
5 - 3 = 2
→ Next three: 5, 3, 2
---
(d) 576, 288, 144, 72, ___, ___, ___
Divide by 2 each time:
- 576 ÷ 2 = 288
- 288 ÷ 2 = 144
- 144 ÷ 2 = 72
- 72 ÷ 2 = 36
- 36 ÷ 2 = 18
- 18 ÷ 2 = 9
→ Next three: 36, 18, 9
---
(e) 47, 40, 45, 38, 43, 36, 41, ___, ___, ___
Pattern: alternate between subtracting 7 and adding 5?
Let’s check:
47 → 40 (–7)
40 → 45 (+5)
45 → 38 (–7)
38 → 43 (+5)
43 → 36 (–7)
36 → 41 (+5)
41 → ? (should be –7) → 34
34 → ? (+5) → 39
39 → ? (–7) → 32
→ Next three: 34, 39, 32
---
EXERCISE 3
(a) 2, 3, 5, 7, 11, ___, ___
These are prime numbers! Next primes after 11: 13, 17
→ Next two: 13, 17
---
(b) 21, 22, 24, 25, 26, ___, ___
Looks like skip some numbers? Let’s see differences:
21 to 22: +1
22 to 24: +2
24 to 25: +1
25 to 26: +1
Hmm… maybe not consistent.
Wait — perhaps it’s increasing by 1, then 2, then 1, then 1... that doesn’t help.
Alternative idea: Maybe it’s all numbers except multiples of 3? Let’s check:
21 (div by 3), 22 (ok), 24 (div by 3), 25 (ok), 26 (ok) — no, 21 and 24 are included.
Another idea: Maybe it’s just counting up but skipping nothing? But 21,22,24 — skipped 23? Then 24,25,26 — so maybe next is 27,28?
But why skip 23? That doesn’t fit.
Wait — let’s list positions:
Position 1: 21
Position 2: 22
Position 3: 24 ← jumped over 23
Position 4: 25
Position 5: 26
Maybe position 6: 27? Position 7: 28?
But why jump only once? Not clear.
Alternative: Maybe it’s “numbers that are not divisible by 3” — but 21 and 24 ARE divisible by 3.
Wait — perhaps typo? Or maybe it’s +1, +2, +1, +1, then +1, +1?
From 26, if we continue +1: 27, 28
But let’s look again: 21,22,24,25,26 — maybe it’s supposed to be 21,22,23,24,25,26? But 23 is missing.
Perhaps it’s a mistake? Or maybe it’s “add 1, add 2, add 1, add 1, add 1, add 1…” — unlikely.
Another thought: Maybe it’s the sequence of numbers where digit sum is not divisible by 3? Too complicated.
Wait — let’s try this: from 21 to 22: +1
22 to 24: +2
24 to 25: +1
25 to 26: +1
Then maybe next: +1 → 27, +1 → 28? But why the +2 earlier?
Perhaps it’s a typo and should be 21,22,23,24,25,26 — then next would be 27,28.
Given that, and since 23 is missing, maybe it’s intentional? Let’s assume the pattern is mostly +1, with one +2 early on — but that’s weak.
Alternatively, think of it as: starting at 21, then every number except those ending in 3? 23 is skipped, next would be 27,28? But 27 ends in 7, 28 in 8 — no reason to skip.
I think the most reasonable assumption is that it’s simply counting up, and 23 was accidentally skipped — or perhaps it’s meant to be 21,22,23,24,25,26 — but since 23 is missing, maybe the pattern is “skip every third number”? Let’s test:
Start at 21 (keep), 22 (keep), 23 (skip), 24 (keep), 25 (keep), 26 (keep), 27 (skip?), 28 (keep), 29 (keep)... but that doesn’t match because 24,25,26 are kept.
Actually, looking back: 21,22,24,25,26 — that’s five numbers. If we consider the gap between 22 and 24 is +2, others +1, perhaps it’s irregular.
But let’s notice: 21,22, then skip 23, then 24,25,26 — so maybe next is 27,28? I think that’s safest.
Or perhaps it’s “all numbers from 21 onward except 23” — then next are 27,28? No, 27 comes after 26.
After 26, next natural numbers are 27,28.
I’ll go with 27, 28 — assuming the skip of 23 was a one-time thing or error.
But wait — another idea: maybe it’s numbers whose English name has even letters? Too complex.
Let me check online or standard patterns — but since I can’t, I’ll assume it’s +1,+2,+1,+1,+1,... so after 26, +1=27, +1=28.
→ Next two: 27, 28
*(Note: This one is ambiguous, but 27,28 is most logical continuation)*
---
(c) 1, 4, 9, 16, 25, ___, ___
Perfect squares:
1²=1, 2²=4, 3²=9, 4²=16, 5²=25
Next: 6²=36, 7²=49
→ Next two: 36, 49
---
(d) 47, 49, 51, 53, 55, 57, ___, ___
Odd numbers increasing by 2:
47,49,51,53,55,57 — next odd numbers: 59, 61
→ Next two: 59, 61
---
(e) 1, 8, 27, 64, ___, ___
Cubes:
1³=1, 2³=8, 3³=27, 4³=64
Next: 5³=125, 6³=216
→ Next two: 125, 216
---
(f) 53, 59, 61, 67, ___, ___
Prime numbers! Let’s list primes around there:
Primes: 53, 59, 61, 67, next is 71, then 73
Check: 53 (prime), 59 (prime), 61 (prime), 67 (prime), then 71, 73
Yes!
→ Next two: 71, 73
---
Final Answer:
EXERCISE 1
(a) 32, 64, 128
(b) 13, 16, 19
(c) 35, 42, 49
(d) 20000, 200000, 2000000
(e) 30, 36, 42
EXERCISE 2
(a) 78, 73, 83
(b) 61, 99, 160
(c) 5, 3, 2
(d) 36, 18, 9
(e) 34, 39, 32
EXERCISE 3
(a) 13, 17
(b) 27, 28
(c) 36, 49
(d) 59, 61
(e) 125, 216
(f) 71, 73
---
EXERCISE 1
(a) 2, 4, 8, 16, ___, ___, ___
Each number is multiplied by 2:
- 2 × 2 = 4
- 4 × 2 = 8
- 8 × 2 = 16
- 16 × 2 = 32
- 32 × 2 = 64
- 64 × 2 = 128
→ Next three: 32, 64, 128
---
(b) 1, 4, 7, 10, ___, ___, ___
Each number increases by 3:
- 1 + 3 = 4
- 4 + 3 = 7
- 7 + 3 = 10
- 10 + 3 = 13
- 13 + 3 = 16
- 16 + 3 = 19
→ Next three: 13, 16, 19
---
(c) 7, 14, 21, 28, ___, ___, ___
Multiples of 7:
- 7×1=7, 7×2=14, 7×3=21, 7×4=28
- 7×5 = 35
- 7×6 = 42
- 7×7 = 49
→ Next three: 35, 42, 49
---
(d) 2, 20, 200, 2000, ___, ___, ___
Each number is multiplied by 10:
- 2 × 10 = 20
- 20 × 10 = 200
- 200 × 10 = 2000
- 2000 × 10 = 20000
- 20000 × 10 = 200000
- 200000 × 10 = 2000000
→ Next three: 20000, 200000, 2000000
---
(e) 6, 12, 18, 24, ___, ___, ___
Multiples of 6:
- 6×1=6, 6×2=12, 6×3=18, 6×4=24
- 6×5 = 30
- 6×6 = 36
- 6×7 = 42
→ Next three: 30, 36, 42
---
EXERCISE 2
(a) 58, 68, 63, 73, 68, ___, ___, ___
Look at the pattern:
+10, -5, +10, -5, ...
So:
- 58 +10 = 68
- 68 -5 = 63
- 63 +10 = 73
- 73 -5 = 68
- 68 +10 = 78
- 78 -5 = 73
- 73 +10 = 83
→ Next three: 78, 73, 83
---
(b) 7, 8, 15, 23, 38, ___, ___, ___
This looks like Fibonacci-style: add previous two numbers.
Check:
- 7 + 8 = 15 ✔
- 8 + 15 = 23 ✔
- 15 + 23 = 38 ✔
- 23 + 38 = 61
- 38 + 61 = 99
- 61 + 99 = 160
→ Next three: 61, 99, 160
---
(c) 55, 34, 21, 13, 8, ___, ___, ___
Subtracting: each number is the difference of the two before? Or going down?
Actually, this is reverse Fibonacci:
55 - 34 = 21
34 - 21 = 13
21 - 13 = 8
13 - 8 = 5
8 - 5 = 3
5 - 3 = 2
→ Next three: 5, 3, 2
---
(d) 576, 288, 144, 72, ___, ___, ___
Divide by 2 each time:
- 576 ÷ 2 = 288
- 288 ÷ 2 = 144
- 144 ÷ 2 = 72
- 72 ÷ 2 = 36
- 36 ÷ 2 = 18
- 18 ÷ 2 = 9
→ Next three: 36, 18, 9
---
(e) 47, 40, 45, 38, 43, 36, 41, ___, ___, ___
Pattern: alternate between subtracting 7 and adding 5?
Let’s check:
47 → 40 (–7)
40 → 45 (+5)
45 → 38 (–7)
38 → 43 (+5)
43 → 36 (–7)
36 → 41 (+5)
41 → ? (should be –7) → 34
34 → ? (+5) → 39
39 → ? (–7) → 32
→ Next three: 34, 39, 32
---
EXERCISE 3
(a) 2, 3, 5, 7, 11, ___, ___
These are prime numbers! Next primes after 11: 13, 17
→ Next two: 13, 17
---
(b) 21, 22, 24, 25, 26, ___, ___
Looks like skip some numbers? Let’s see differences:
21 to 22: +1
22 to 24: +2
24 to 25: +1
25 to 26: +1
Hmm… maybe not consistent.
Wait — perhaps it’s increasing by 1, then 2, then 1, then 1... that doesn’t help.
Alternative idea: Maybe it’s all numbers except multiples of 3? Let’s check:
21 (div by 3), 22 (ok), 24 (div by 3), 25 (ok), 26 (ok) — no, 21 and 24 are included.
Another idea: Maybe it’s just counting up but skipping nothing? But 21,22,24 — skipped 23? Then 24,25,26 — so maybe next is 27,28?
But why skip 23? That doesn’t fit.
Wait — let’s list positions:
Position 1: 21
Position 2: 22
Position 3: 24 ← jumped over 23
Position 4: 25
Position 5: 26
Maybe position 6: 27? Position 7: 28?
But why jump only once? Not clear.
Alternative: Maybe it’s “numbers that are not divisible by 3” — but 21 and 24 ARE divisible by 3.
Wait — perhaps typo? Or maybe it’s +1, +2, +1, +1, then +1, +1?
From 26, if we continue +1: 27, 28
But let’s look again: 21,22,24,25,26 — maybe it’s supposed to be 21,22,23,24,25,26? But 23 is missing.
Perhaps it’s a mistake? Or maybe it’s “add 1, add 2, add 1, add 1, add 1, add 1…” — unlikely.
Another thought: Maybe it’s the sequence of numbers where digit sum is not divisible by 3? Too complicated.
Wait — let’s try this: from 21 to 22: +1
22 to 24: +2
24 to 25: +1
25 to 26: +1
Then maybe next: +1 → 27, +1 → 28? But why the +2 earlier?
Perhaps it’s a typo and should be 21,22,23,24,25,26 — then next would be 27,28.
Given that, and since 23 is missing, maybe it’s intentional? Let’s assume the pattern is mostly +1, with one +2 early on — but that’s weak.
Alternatively, think of it as: starting at 21, then every number except those ending in 3? 23 is skipped, next would be 27,28? But 27 ends in 7, 28 in 8 — no reason to skip.
I think the most reasonable assumption is that it’s simply counting up, and 23 was accidentally skipped — or perhaps it’s meant to be 21,22,23,24,25,26 — but since 23 is missing, maybe the pattern is “skip every third number”? Let’s test:
Start at 21 (keep), 22 (keep), 23 (skip), 24 (keep), 25 (keep), 26 (keep), 27 (skip?), 28 (keep), 29 (keep)... but that doesn’t match because 24,25,26 are kept.
Actually, looking back: 21,22,24,25,26 — that’s five numbers. If we consider the gap between 22 and 24 is +2, others +1, perhaps it’s irregular.
But let’s notice: 21,22, then skip 23, then 24,25,26 — so maybe next is 27,28? I think that’s safest.
Or perhaps it’s “all numbers from 21 onward except 23” — then next are 27,28? No, 27 comes after 26.
After 26, next natural numbers are 27,28.
I’ll go with 27, 28 — assuming the skip of 23 was a one-time thing or error.
But wait — another idea: maybe it’s numbers whose English name has even letters? Too complex.
Let me check online or standard patterns — but since I can’t, I’ll assume it’s +1,+2,+1,+1,+1,... so after 26, +1=27, +1=28.
→ Next two: 27, 28
*(Note: This one is ambiguous, but 27,28 is most logical continuation)*
---
(c) 1, 4, 9, 16, 25, ___, ___
Perfect squares:
1²=1, 2²=4, 3²=9, 4²=16, 5²=25
Next: 6²=36, 7²=49
→ Next two: 36, 49
---
(d) 47, 49, 51, 53, 55, 57, ___, ___
Odd numbers increasing by 2:
47,49,51,53,55,57 — next odd numbers: 59, 61
→ Next two: 59, 61
---
(e) 1, 8, 27, 64, ___, ___
Cubes:
1³=1, 2³=8, 3³=27, 4³=64
Next: 5³=125, 6³=216
→ Next two: 125, 216
---
(f) 53, 59, 61, 67, ___, ___
Prime numbers! Let’s list primes around there:
Primes: 53, 59, 61, 67, next is 71, then 73
Check: 53 (prime), 59 (prime), 61 (prime), 67 (prime), then 71, 73
Yes!
→ Next two: 71, 73
---
Final Answer:
EXERCISE 1
(a) 32, 64, 128
(b) 13, 16, 19
(c) 35, 42, 49
(d) 20000, 200000, 2000000
(e) 30, 36, 42
EXERCISE 2
(a) 78, 73, 83
(b) 61, 99, 160
(c) 5, 3, 2
(d) 36, 18, 9
(e) 34, 39, 32
EXERCISE 3
(a) 13, 17
(b) 27, 28
(c) 36, 49
(d) 59, 61
(e) 125, 216
(f) 71, 73
Parent Tip: Review the logic above to help your child master the concept of patterns and sequences worksheet.
