In this article, we will explore how to find the sum of the first 10 even numbers using a step-by-step approach. This is a common arithmetic sequence problem that can be easily solved with a simple formula.
How to Find the Sum of the First 10 Even Numbers
By the end of this guide, you’ll be able to calculate the sum of any series of even numbers with confidence.
Step 1: Identify the First 10 Even Numbers
Before we can calculate the sum of the first 10 even numbers, we need to know what these numbers are. An even number is any integer that is divisible by 2. To find the first 10 even numbers, we can start at 2 (the first even number) and proceed in increments of 2:
- 2
- 4
- 6
- 8
- 10
- 12
- 14
- 16
- 18
- 20
Now that we’ve listed the first 10 even numbers, we can move on to finding their sum.
Step 2: Understand the Arithmetic Sequence
An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant. In this case, the first 10 even numbers form an arithmetic sequence with a common difference of 2.
To find the sum of an arithmetic sequence, we can use the formula:
Sum = (n * (a1 + an)) / 2
Where:
- n is the number of terms in the sequence
- a1 is the first term in the sequence
- an is the last term in the sequence
Step 3: Apply the Arithmetic Sequence Formula
We can now use the arithmetic sequence formula to find the sum of the first 10 even numbers:
n = 10 (since there are 10 even numbers) a1 = 2 (the first even number) an = 20 (the last even number)
Sum = (10 * (2 + 20)) / 2
Step 4: Calculate the Sum
Perform the arithmetic operations to find the sum:
Sum = (10 * 22) / 2 Sum = 220 / 2 Sum = 110
The sum of the first 10 even numbers is 110.
Conclusion
In this article, we’ve learned how to find the sum of the first 10 even numbers using a step-by-step approach. By identifying the arithmetic sequence and applying the appropriate formula, we were able to calculate the sum with ease.
This method can be applied to any arithmetic sequence, making it a valuable tool for solving a variety of mathematical problems. Remember to practice and apply these concepts to other arithmetic sequences to further develop your mathematical skills.