What is the sum of odd numbers from 10 to 165? Here we will show you step-by-step how to calculate the sum of odd numbers from 10 to 165.
Step 1) We start by finding the first (F) and last (L) odd numbers from 10 to 165. It is easy to do that by simply looking at the numbers. The first odd number is 11, and the last odd number is 165.
F = 11
L = 165
Step 2) Next, we calculate the total odd numbers (T) there are from 10 to 165, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (165 - 11 + 2) ÷ 2
T = 156 ÷ 2
T = 78
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 165, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (78 ÷ 2) × (2 × 11 + (2 × (78 - 1))
Sum = 39 × (22 + 154)
Sum = 39 × 176
Sum = 6864
Sum of odd numbers from 10 to 165 = 6864
Sum of Odd Numbers Calculator
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