SOLUTION: What is the sum of all consecutive even integers between 1 and 100 inclusive?

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Question 923653: What is the sum of all consecutive even integers between 1 and 100 inclusive?
Found 3 solutions by josmiceli, MathLover1, MathTherapy:
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website!
Suppose you have:

The sum is
The formula for this is:

where is the last number
check:

OK
Now use it for numbers 1 to 100

Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
Sum of all consecutive integers:

SUM OF NUMBERS:
Formula:
How to Find
in your case:
+...+
find how many even numbers we have from to

go to and find a sum of first positive integers =>

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

What is the sum of all consecutive even integers between 1 and 100 inclusive?

The numbers to be summed begin at 2, and end at 100, inclusive
Using the sum of an AP series formula: , where:
is the sum of the numbers in the series
is the number of numbers in the series
is the first term in the series
is the common difference between each CONSECUTIVE term
Number of consecutive even numbers in the set: , or , or 50
Therefore, becomes:

Sum of series, or