What is the sum of odd numbers from 3 to 164? Here we will show you step-by-step how to calculate the sum of odd numbers from 3 to 164.
Step 1) We start by finding the first (F) and last (L) odd numbers from 3 to 164. It is easy to do that by simply looking at the numbers. The first odd number is 3, and the last odd number is 163.
F = 3
L = 163
Step 2) Next, we calculate the total odd numbers (T) there are from 3 to 164, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (163 - 3 + 2) ÷ 2
T = 162 ÷ 2
T = 81
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 164, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (81 ÷ 2) × (2 × 3 + (2 × (81 - 1))
Sum = 40.5 × (6 + 160)
Sum = 40.5 × 166
Sum = 6723
Sum of odd numbers from 3 to 164 = 6723
Sum of Odd Numbers Calculator
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