Calculate the sum of all even natural number from 2 to 74

To calculate the sum of all even natural numbers from 2 to 74, we can use the formula for the sum of an arithmetic sequence. 

The even numbers from 2 to 74 form the sequence:  
\[ 2, 4, 6, \dots, 74 \]

This is an arithmetic sequence where:  
- The first term \( a = 2 \)  
- The common difference \( d = 2 \)  
- The last term \( l = 74 \)

### Step 1: Find the number of terms
The number of terms \( n \) in an arithmetic sequence is given by the formula:  
\[ n = \frac{l - a}{d} + 1 \]

Substitute the values:  
\[ n = \frac{74 - 2}{2} + 1 = \frac{72}{2} + 1 = 36 + 1 = 37 \]

So, there are 37 terms in this sequence.

### Step 2: Use the sum formula for an arithmetic sequence
The sum \( S \) of the first \( n \) terms of an arithmetic sequence is given by:  
\[ S = \frac{n}{2} \times (a + l) \]

Substitute the values:  
\[ S = \frac{37}{2} \times (2 + 74) = \frac{37}{2} \times 76 = 37 \times 38 = 1406 \]

### Final Answer:
The sum of all even natural numbers from 2 to 74 is **1406**.

Would you like further explanation on any step? Or have additional questions?  
Here are a few related topics you might find interesting:

1. How to find the sum of odd numbers in a sequence.
2. How to calculate the sum of a geometric series.
3. The relationship between the sum of even numbers and the sum of all integers.
4. How to use arithmetic sequences in real-world problems.
5. How to find the sum of numbers divisible by a specific integer.

**Tip:** When calculating the sum of a sequence, always identify the first term, common difference, and last term to use the arithmetic sum formula effectively!

Calculate the sum of all even natural numbers from 2 to 74

Learn how to calculate the sum of all even natural numbers from 2 to 74 using the arithmetic sequence sum formula. This solution explains step-by-step how to find the number of terms and apply the formula for the sum of an arithmetic sequence. Suitable for students in Grades 6-8.

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