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In the Collatz sequence starting from 21, what is the fourth number?
- a)16
- b)32
- c)64
- d)42
Correct answer is option 'A'. Can you explain this answer?
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In the Collatz sequence starting from 21, what is the fourth number?a)...
Understanding the Collatz Sequence
The Collatz sequence (also known as the 3n + 1 sequence) is generated from any positive integer by following these simple rules:
- If the number is even, divide it by 2.
- If the number is odd, multiply it by 3 and add 1.
The sequence continues until it reaches 1.
Starting from 21
Let's generate the Collatz sequence starting from 21:
1. First number (21):
- Since 21 is odd, we use the odd rule:
- 3 * 21 + 1 = 63 + 1 = 64.
2. Second number (64):
- Now, 64 is even, so we divide it by 2:
- 64 / 2 = 32.
3. Third number (32):
- 32 is even, so we divide it by 2 again:
- 32 / 2 = 16.
4. Fourth number (16):
- 16 is even, and dividing by 2 gives us:
- 16 / 2 = 8.
Thus, the sequence starting from 21 is as follows:
- 21 → 64 → 32 → 16 → 8 ...
Conclusion
From the sequence, the fourth number is 16. Therefore, the correct answer is option 'A'.
The Collatz sequence (also known as the 3n + 1 sequence) is generated from any positive integer by following these simple rules:
- If the number is even, divide it by 2.
- If the number is odd, multiply it by 3 and add 1.
The sequence continues until it reaches 1.
Starting from 21
Let's generate the Collatz sequence starting from 21:
1. First number (21):
- Since 21 is odd, we use the odd rule:
- 3 * 21 + 1 = 63 + 1 = 64.
2. Second number (64):
- Now, 64 is even, so we divide it by 2:
- 64 / 2 = 32.
3. Third number (32):
- 32 is even, so we divide it by 2 again:
- 32 / 2 = 16.
4. Fourth number (16):
- 16 is even, and dividing by 2 gives us:
- 16 / 2 = 8.
Thus, the sequence starting from 21 is as follows:
- 21 → 64 → 32 → 16 → 8 ...
Conclusion
From the sequence, the fourth number is 16. Therefore, the correct answer is option 'A'.
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Community Answer
In the Collatz sequence starting from 21, what is the fourth number?a)...
The sequence starting from 21 follows 21 → 64 → 32 → 16. The fourth number in the sequence is 16.
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In the Collatz sequence starting from 21, what is the fourth number?a)16b)32c)64d)42Correct answer is option 'A'. Can you explain this answer?
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