What is the sum of even numbers from 1 to 101? Here we will show you step-by-step how to calculate the sum of even numbers from 1 to 101.
Step 1) We start by finding the first (F) and last (L) even numbers from 1 to 101. It is easy to do that by simply looking at the numbers. The first even number is 2, and the last even number is 100.
F = 2
L = 100
Step 2) Next, we calculate the total even numbers (T) there are from 1 to 101, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (100 - 2 + 2) ÷ 2
T = 100 ÷ 2
T = 50
Step 3) Finally, we use the information from Step 1 and Step 2, and another formula, to calculate the sum of even numbers from 1 to 101, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (50 ÷ 2) × (2 × 2 + (2 × (50 - 1))
Sum = 25 × (4 + 98)
Sum = 25 × 102
Sum = 2550
Sum of even numbers from 1 to 101 = 2550
Sum of Even Numbers Calculator
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