Meaning of term the sum of p even no. Is even.

The phrase "the sum of \( p \) even numbers is even" means that when you add together any \( p \) even numbers, the result will always be an even number.

### Why is this true?

- **Even numbers** are numbers that can be divided by 2 without leaving a remainder. For example, 2, 4, 6, 8, etc.
- When you add two even numbers together, the result is always even. This happens because both numbers are divisible by 2, so their sum remains divisible by 2.
- Extending this, if you add more even numbers (any \( p \) even numbers), their sum will also remain divisible by 2, so the result will still be an even number.

### Example:
- Let's say \( p = 3 \) and you choose the even numbers 2, 4, and 6.
  \[
  2 + 4 + 6 = 12
  \]
  Since 12 is an even number, this satisfies the statement.

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### Relative Questions:
1. What happens when you add an even number to an odd number?
2. How can you prove that the sum of even numbers is always even algebraically?
3. What is the sum of the first \( n \) even numbers?
4. What is the difference between the sum of odd and even numbers?
5. How do we define an even number mathematically?

### Tip:
When adding a sequence of numbers, remember that the parity (evenness or oddness) of the result depends on the types of numbers being summed.

Meaning of term the sum of p even no. is even.

Discover why the sum of p even numbers always results in an even number. This concept explores the fundamental idea of number parity and how even numbers behave when added. Suitable for Grades 5-7.

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