What is the sum of odd numbers from 3 to 165? Here we will show you step-by-step how to calculate the sum of odd numbers from 3 to 165.
Step 1) We start by finding the first (F) and last (L) odd numbers from 3 to 165. It is easy to do that by simply looking at the numbers. The first odd number is 3, and the last odd number is 165.
F = 3
L = 165
Step 2) Next, we calculate the total odd numbers (T) there are from 3 to 165, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (165 - 3 + 2) ÷ 2
T = 164 ÷ 2
T = 82
Step 3) Finally, we use the information from Step 1 and Step 2, and another formula, to calculate the sum of odd numbers from 3 to 165, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (82 ÷ 2) × (2 × 3 + (2 × (82 - 1))
Sum = 41 × (6 + 162)
Sum = 41 × 168
Sum = 6888
Sum of odd numbers from 3 to 165 = 6888
Sum of Odd Numbers Calculator
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