What is the sum of odd numbers from 1 to 105? Here we will show you step-by-step how to calculate the sum of odd numbers from 1 to 105.
Step 1) We start by finding the first (F) and last (L) odd numbers from 1 to 105. It is easy to do that by simply looking at the numbers. The first odd number is 1, and the last odd number is 105.
F = 1
L = 105
Step 2) Next, we calculate the total odd numbers (T) there are from 1 to 105, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (105 - 1 + 2) ÷ 2
T = 106 ÷ 2
T = 53
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 105, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (53 ÷ 2) × (2 × 1 + (2 × (53 - 1))
Sum = 26.5 × (2 + 104)
Sum = 26.5 × 106
Sum = 2809
Sum of odd numbers from 1 to 105 = 2809
Sum of Odd Numbers Calculator
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