What is the sum of odd numbers from 10 to 85? Here we will show you step-by-step how to calculate the sum of odd numbers from 10 to 85.
Step 1) We start by finding the first (F) and last (L) odd numbers from 10 to 85. It is easy to do that by simply looking at the numbers. The first odd number is 11, and the last odd number is 85.
F = 11
L = 85
Step 2) Next, we calculate the total odd numbers (T) there are from 10 to 85, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (85 - 11 + 2) ÷ 2
T = 76 ÷ 2
T = 38
Step 3) Finally, we use the information from Step 1 and Step 2, and another formula, to calculate the sum of odd numbers from 10 to 85, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (38 ÷ 2) × (2 × 11 + (2 × (38 - 1))
Sum = 19 × (22 + 74)
Sum = 19 × 96
Sum = 1824
Sum of odd numbers from 10 to 85 = 1824
Sum of Odd Numbers Calculator
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