Let's solve
Newton's Number Track Puzzle 2 step by step.
🔍 Rule Recap:
Each number in the sequence is the
sum of the two previous numbers.
This is similar to the Fibonacci sequence.
We'll go through each track one by one and fill in the missing numbers.
---
✔ 1) 4, 5, 9, __, __
- 4 + 5 = 9
✔ (already given)
- 5 + 9 =
14
- 9 + 14 =
23
✔ Answer: 4, 5, 9,
14,
23
---
✔ 2) 9, 2, __, __, __
- 9 + 2 =
11
- 2 + 11 =
13
- 11 + 13 =
24
✔ Answer: 9, 2,
11,
13,
24
---
✔ 3) 3, 6, __, __, __
- 3 + 6 =
9
- 6 + 9 =
15
- 9 + 15 =
24
✔ Answer: 3, 6,
9,
15,
24
---
✔ 4) 8, 5, __, __, __
- 8 + 5 =
13
- 5 + 13 =
18
- 13 + 18 =
31
✔ Answer: 8, 5,
13,
18,
31
---
✔ 5) 4, 7, __, __, __
- 4 + 7 =
11
- 7 + 11 =
18
- 11 + 18 =
29
✔ Answer: 4, 7,
11,
18,
29
---
✔ 6) 5, 6, __, __, __
- 5 + 6 =
11
- 6 + 11 =
17
- 11 + 17 =
28
✔ Answer: 5, 6,
11,
17,
28
---
✔ 7) 11, 0, __, __, __
- 11 + 0 =
11
- 0 + 11 =
11
- 11 + 11 =
22
✔ Answer: 11, 0,
11,
11,
22
---
✔ 8) 3, __, 9, __, __
We have:
- First number: 3
- Third number: 9
Let the second number be
x
Then:
- 3 + x = 9 → x =
6
Now continue:
- 3, 6, 9
- 6 + 9 =
15
- 9 + 15 =
24
✔ Answer: 3,
6, 9,
15,
24
---
✔ 9) __, 7, 12, __, __
Let the first number be
x
We know:
- x + 7 = 12 → x =
5
Now:
- 5, 7, 12
- 7 + 12 =
19
- 12 + 19 =
31
✔ Answer: 5, 7, 12,
19,
31
---
✔ 10) 6, __, __, __, 21
Let’s denote the unknowns:
- a₁ = 6
- a₂ = ?
- a₃ = ?
- a₄ = ?
- a₅ = 21
We use the rule:
a₃ = a₁ + a₂
a₄ = a₂ + a₃
a₅ = a₃ + a₄ = 21
Let’s let a₂ = x
Then:
- a₃ = 6 + x
- a₄ = x + (6 + x) = 6 + 2x
- a₅ = (6 + x) + (6 + 2x) = 12 + 3x
But a₅ = 21 →
12 + 3x = 21
3x = 9
x = 3
So:
- a₂ = 3
- a₃ = 6 + 3 = 9
- a₄ = 3 + 9 = 12
- a₅ = 9 + 12 = 21
✔
✔ Answer: 6,
3,
9,
12, 21
---
✔ Final Answers:
1) 4, 5, 9,
14,
23
2) 9, 2,
11,
13,
24
3) 3, 6,
9,
15,
24
4) 8, 5,
13,
18,
31
5) 4, 7,
11,
18,
29
6) 5, 6,
11,
17,
28
7) 11, 0,
11,
11,
22
8) 3,
6, 9,
15,
24
9)
5, 7, 12,
19,
31
10) 6,
3,
9,
12, 21
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Let me know if you'd like this as a printable answer sheet! 😊
Parent Tip: Review the logic above to help your child master the concept of 2 grade puzzles.
