The sum of even numbers can be found using a formula derived from arithmetic progression or by iteratively adding them. Let's explore both methods.
Formula Method: Using Arithmetic Progression
Even numbers form an arithmetic progression (AP) with a common difference of 2 (2, 4, 6, 8,...). The formula to calculate the sum is:
Sum of Even Numbers = n(n + 1)
Where 'n' is the number of even numbers you want to sum.
Example:
Let's say you want to find the sum of the first 5 even numbers (2, 4, 6, 8, 10).
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n = 5
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Sum = 5 (5 + 1) = 5 6 = 30
Therefore, the sum of the first 5 even numbers is 30.
Iterative Method: Direct Addition
If you have a specific set of even numbers, you can simply add them together.
Example:
Find the sum of 2, 4, 6, and 8.
Sum = 2 + 4 + 6 + 8 = 20
Choosing the Right Method
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Formula: Use the formula
n(n+1)when you need to find the sum of the first n even numbers. This is the most efficient method when you know the count of even numbers you need to sum from the beginning of the sequence (2, 4, 6, ...). -
Direct Addition: Use direct addition when you have a specific, possibly non-sequential, set of even numbers. This is also suitable if you have a small number of even numbers to add, where applying the formula might be less efficient.
Summary
To find the sum of even numbers, you can use the formula n(n+1) where 'n' represents the number of even numbers (starting from 2) you want to sum. Alternatively, you can add the even numbers together directly if you have a specific set.
