What is the sum of odd numbers from 20 to 105? Here we will show you step-by-step how to calculate the sum of odd numbers from 20 to 105.
Step 1) We start by finding the first (F) and last (L) odd numbers from 20 to 105. It is easy to do that by simply looking at the numbers. The first odd number is 21, and the last odd number is 105.
F = 21
L = 105
Step 2) Next, we calculate the total odd numbers (T) there are from 20 to 105, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (105 - 21 + 2) ÷ 2
T = 86 ÷ 2
T = 43
Step 3) Finally, we use the information from Step 1 and Step 2, and another formula, to calculate the sum of odd numbers from 20 to 105, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (43 ÷ 2) × (2 × 21 + (2 × (43 - 1))
Sum = 21.5 × (42 + 84)
Sum = 21.5 × 126
Sum = 2709
Sum of odd numbers from 20 to 105 = 2709
Sum of Odd Numbers Calculator
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