हिंदी में जवाब दो: Explain why the sum of any three consecutive whole numbers is always divisible by 3. Illustrate your reasoning with two examples.

Answer: The sum of any three consecutive whole numbers is always divisible by 3 because their sum can be expressed as $3(n+1)$ , which is a multiple of 3. For example, $4+5+6=15$ (divisible by 3) and $10+11+12=33$ (divisible by 3).

Step-by-step solution

Step 1: Representing Consecutive Whole Numbers

Let's represent any whole number as $n$ . Then, the next two consecutive whole numbers will be $n+1$ and $n+2$ . These three expressions represent any three consecutive whole numbers.

Step 2: Finding the Sum

Now, we need to find the sum of these three consecutive whole numbers. We add the three expressions together.

Step 3: Simplifying the Sum

When we add $n$ , $n+1$ , and $n+2$ , we get $3n+3$ . We can factor out 3 from this expression, which gives us $3(n+1)$ .

Step 4: Conclusion on Divisibility

Since the sum can be written as $3(n+1)$ , it means the sum is always a multiple of 3. Therefore, the sum of any three consecutive whole numbers is always divisible by 3.

Step 5: Example 1

Let's take an example with the numbers 4, 5, and 6. Their sum is $4+5+6 = 15$ . When we divide 15 by 3, we get 5, which confirms that 15 is divisible by 3.

Step 6: Example 2

For another example, consider the numbers 10, 11, and 12. Their sum is $10+11+12 = 33$ . Dividing 33 by 3 gives us 11, again showing that the sum is divisible by 3.

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