What is the sum of odd numbers from 1 to 100? Here we will show you step-by-step how to calculate the sum of odd numbers from 1 to 100.
Step 1) We start by finding the first (F) and last (L) odd numbers from 1 to 100. It is easy to do that by simply looking at the numbers. The first odd number is 1, and the last odd number is 99.
F = 1
L = 99
Step 2) Next, we calculate the total odd numbers (T) there are from 1 to 100, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (99 - 1 + 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 odd numbers from 1 to 100, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (50 ÷ 2) × (2 × 1 + (2 × (50 - 1))
Sum = 25 × (2 + 98)
Sum = 25 × 100
Sum = 2500
Sum of odd numbers from 1 to 100 = 2500
Sum of Odd Numbers Calculator
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