Number Patterns & Sequences | brmackey | Live - Free Printable

Sure! Let’s solve each exercise step by step, identifying the pattern in each sequence and filling in the missing numbers.

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## EXERCISE 1: Complete each number sequence by filling in the next three numbers.

(a) 2, 4, 8, 16, __, __, __

Pattern: Each number is multiplied by 2.
→ 16 × 2 = 32
→ 32 × 2 = 64
→ 64 × 2 = 128
✔ Answer: 32, 64, 128

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(b) 1, 4, 7, 10, __, __, __

Pattern: Add 3 each time.
→ 10 + 3 = 13
→ 13 + 3 = 16
→ 16 + 3 = 19
✔ Answer: 13, 16, 19

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(c) 7, 14, 21, 28, __, __, __

Pattern: Multiples of 7 (add 7 each time).
→ 28 + 7 = 35
→ 35 + 7 = 42
→ 42 + 7 = 49
✔ Answer: 35, 42, 49

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(d) 2, 20, 200, 2000, __, __, __

Pattern: Multiply by 10 each time.
→ 2000 × 10 = 20,000
→ 20,000 × 10 = 200,000
→ 200,000 × 10 = 2,000,000
✔ Answer: 20000, 200000, 2000000

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(e) 6, 12, 18, 24, __, __, __

Pattern: Multiples of 6 (add 6 each time).
→ 24 + 6 = 30
→ 30 + 6 = 36
→ 36 + 6 = 42
✔ Answer: 30, 36, 42

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## EXERCISE 2: Complete each number sequence by filling in the next three numbers.

(a) 58, 68, 63, 73, 68, __, __, __

Pattern: Alternating +10, -5
→ 68 + 10 = 78
→ 78 - 5 = 73
→ 73 + 10 = 83
✔ Answer: 78, 73, 83

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(b) 7, 6, 15, 23, 38, __, __, __

Pattern: Starting from the 3rd term, each number is the sum of the two previous numbers (Fibonacci-style).
→ 15 + 23 = 38 (already given)
→ 23 + 38 = 61
→ 38 + 61 = 99
→ 61 + 99 = 160
✔ Answer: 61, 99, 160

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(c) 55, 34, 21, 13, 8, __, __, __

Pattern: Each number is the difference of the two previous numbers? Let’s check backwards:
Actually, this looks like Fibonacci *in reverse*:
Each term = previous term - the one before that?
Let’s test:
55 - 34 = 21 ✔️
34 - 21 = 13 ✔️
21 - 13 = 8 ✔️
So next:
→ 13 - 8 = 5
→ 8 - 5 = 3
→ 5 - 3 = 2
✔ Answer: 5, 3, 2

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(d) 576, 288, 144, 72, __, __, __

Pattern: Divide by 2 each time.
→ 72 ÷ 2 = 36
→ 36 ÷ 2 = 18
→ 18 ÷ 2 = 9
✔ Answer: 36, 18, 9

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(e) 47, 40, 45, 38, 43, 36, 41, __, __, __

Pattern: Alternating subtract 7, add 5
→ 47 - 7 = 40
→ 40 + 5 = 45
→ 45 - 7 = 38
→ 38 + 5 = 43
→ 43 - 7 = 36
→ 36 + 5 = 41 (given)
→ 41 - 7 = 34
→ 34 + 5 = 39
→ 39 - 7 = 32
✔ Answer: 34, 39, 32

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## EXERCISE 3: Write the next two numbers in each sequence below.

(a) 2, 3, 5, 7, 11, __, __

Pattern: Prime numbers!
Primes: 2, 3, 5, 7, 11, 13, 17
✔ Answer: 13, 17

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(b) 21, 22, 24, 25, 26, __, __

Pattern: Skip 23? Let’s look:
21 → 22 (+1)
22 → 24 (+2)
24 → 25 (+1)
25 → 26 (+1) — doesn’t fit.
Wait — maybe it’s just counting up but skipping 23?
After 26: 27, 28? But why skip 23?
Alternative: Maybe alternating +1, +2, +1, +1... doesn't hold.
Another idea: Perhaps it's numbers that are not divisible by 3?
21 (div by 3) → no.
Wait — let’s list:
21, 22, 24, 25, 26 — missing 23?
Actually, this might be a typo or trick. But if we assume it’s just increasing by 1 after 24:
26 + 1 = 27, 27 + 1 = 28
But 23 is skipped — perhaps intentional?
Alternatively, maybe it’s numbers with digit sum not divisible by 3? Not likely.
Given context, most plausible: It’s just incrementing, skipping 23 for some reason, then continuing:
→ 26 + 1 = 27, 27 + 1 = 28
✔ Answer: 27, 28

*(Note: If this is meant to be “numbers without digit 3”, 23 is excluded — then 27, 28, 29, 30 (has 3) → so 27, 28. That fits!)*

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(c) 1, 4, 9, 16, 25, __, __

Pattern: Perfect squares!
1²=1, 2²=4, 3²=9, 4²=16, 5²=25
→ 6² = 36, 7² = 49
✔ Answer: 36, 49

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(d) 47, 49, 51, 53, 55, 57, __, __

Pattern: Odd numbers increasing by 2.
→ 57 + 2 = 59, 59 + 2 = 61
✔ Answer: 59, 61

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(e) 1, 8, 27, 64, __, __

Pattern: Cubes of natural numbers!
1³=1, 2³=8, 3³=27, 4³=64
→ 5³ = 125, 6³ = 216
✔ Answer: 125, 216

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(f) 53, 59, 61, 67, __, __

Pattern: Prime numbers starting from 53.
Next primes after 67: 71, 73
✔ Answer: 71, 73

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## ✔ Final Answers Summary:

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

Let me know if you’d like visual diagrams or explanations for any specific pattern!