What is the sum of odd numbers from 1 to 65? Here we will show you step-by-step how to calculate the sum of odd numbers from 1 to 65.
Step 1) We start by finding the first (F) and last (L) odd numbers from 1 to 65. It is easy to do that by simply looking at the numbers. The first odd number is 1, and the last odd number is 65.
F = 1
L = 65
Step 2) Next, we calculate the total odd numbers (T) there are from 1 to 65, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (65 - 1 + 2) ÷ 2
T = 66 ÷ 2
T = 33
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 65, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (33 ÷ 2) × (2 × 1 + (2 × (33 - 1))
Sum = 16.5 × (2 + 64)
Sum = 16.5 × 66
Sum = 1089
Sum of odd numbers from 1 to 65 = 1089
Sum of Odd Numbers Calculator
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