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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?
Verified 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)...
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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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? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about 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? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about 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? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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