Sum of odd numbers from 20 to 123


Sum of odd number

What is the sum of odd numbers from 20 to 123? Here we will show you step-by-step how to calculate the sum of odd numbers from 20 to 123.

Step 1) We start by finding the first (F) and last (L) odd numbers from 20 to 123. It is easy to do that by simply looking at the numbers. The first odd number is 21, and the last odd number is 123.

F = 21
L = 123

Step 2) Next, we calculate the total odd numbers (T) there are from 20 to 123, using a formula. Here is the formula and the math:

T = (L - F + 2) ÷ 2
T = (123 - 21 + 2) ÷ 2
T = 104 ÷ 2
T = 52

Step 3) Finally, we use the information from Step 1 and Step 2, and another formula, to calculate the sum of odd numbers from 20 to 123, like this:

Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (52 ÷ 2) × (2 × 21 + (2 × (52 - 1))
Sum = 26 × (42 + 102)
Sum = 26 × 144
Sum = 3744
Sum of odd numbers from 20 to 123 = 3744


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