What is the sum of odd numbers from 1 to 83? Here we will show you step-by-step how to calculate the sum of odd numbers from 1 to 83.
Step 1) We start by finding the first (F) and last (L) odd numbers from 1 to 83. It is easy to do that by simply looking at the numbers. The first odd number is 1, and the last odd number is 83.
F = 1
L = 83
Step 2) Next, we calculate the total odd numbers (T) there are from 1 to 83, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (83 - 1 + 2) ÷ 2
T = 84 ÷ 2
T = 42
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 83, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (42 ÷ 2) × (2 × 1 + (2 × (42 - 1))
Sum = 21 × (2 + 82)
Sum = 21 × 84
Sum = 1764
Sum of odd numbers from 1 to 83 = 1764
Sum of Odd Numbers Calculator
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