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prove that one of the every 3 consecutive number is divisible by 3.
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prove that one of the every 3 consecutive number is divisible by 3.
Let 3 consecutive positive integers be n, n+1 and n+2Whenever a number is divided by 3, the remainder we get is either 0, or 1, or 2.Therefore: n = 3p or 3p+1 or 3p+2, where p is some integerIf n = 3p, then n is divisible by 3If n = 3p+1, then n+2 = 3p+1+2 = 3p+3 = 3(p+1) is divisible by 3If n = 3p+2, then n+1 = 3p+2+1 = 3p+3 = 3(p+1) is divisible by 3Thus, we can state that one of the numbers among n, n+1 and n+2 is always divisible by 3
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Most Upvoted Answer
prove that one of the every 3 consecutive number is divisible by 3.
Proof that one of every 3 consecutive numbers is divisible by 3:
There are three cases when considering three consecutive numbers:
Case 1:
If the first number in the sequence is divisible by 3, then we are done since one of the numbers is divisible by 3.
Case 2:
If the first number is not divisible by 3, but the second number is divisible by 3, then again, we have one number that is divisible by 3.
Case 3:
If the first two numbers are not divisible by 3, then the sum of the three numbers will be divisible by 3. This is because if we consider the numbers to be \(n, n+1, n+2\), the sum is \(3n+3\), which is clearly divisible by 3.
Therefore, in all three cases, we have at least one number in the sequence of three consecutive numbers that is divisible by 3. This proves that one of every 3 consecutive numbers is divisible by 3.
There are three cases when considering three consecutive numbers:
Case 1:
If the first number in the sequence is divisible by 3, then we are done since one of the numbers is divisible by 3.
Case 2:
If the first number is not divisible by 3, but the second number is divisible by 3, then again, we have one number that is divisible by 3.
Case 3:
If the first two numbers are not divisible by 3, then the sum of the three numbers will be divisible by 3. This is because if we consider the numbers to be \(n, n+1, n+2\), the sum is \(3n+3\), which is clearly divisible by 3.
Therefore, in all three cases, we have at least one number in the sequence of three consecutive numbers that is divisible by 3. This proves that one of every 3 consecutive numbers is divisible by 3.
Community Answer
prove that one of the every 3 consecutive number is divisible by 3.
2+3+4=9. 9is divisible by 3😊😊
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prove that one of the every 3 consecutive number is divisible by 3.
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prove that one of the every 3 consecutive number is divisible by 3. for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about prove that one of the every 3 consecutive number is divisible by 3. covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for prove that one of the every 3 consecutive number is divisible by 3..
prove that one of the every 3 consecutive number is divisible by 3. for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about prove that one of the every 3 consecutive number is divisible by 3. covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for prove that one of the every 3 consecutive number is divisible by 3..
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