What is the sum of odd numbers from 20 to 138? Here we will show you step-by-step how to calculate the sum of odd numbers from 20 to 138.
Step 1) We start by finding the first (F) and last (L) odd numbers from 20 to 138. It is easy to do that by simply looking at the numbers. The first odd number is 21, and the last odd number is 137.
F = 21
L = 137
Step 2) Next, we calculate the total odd numbers (T) there are from 20 to 138, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (137 - 21 + 2) ÷ 2
T = 118 ÷ 2
T = 59
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 138, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (59 ÷ 2) × (2 × 21 + (2 × (59 - 1))
Sum = 29.5 × (42 + 116)
Sum = 29.5 × 158
Sum = 4661
Sum of odd numbers from 20 to 138 = 4661
Sum of Odd Numbers Calculator
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