What is the sum of odd numbers from 3 to 21? Here we will show you step-by-step how to calculate the sum of odd numbers from 3 to 21.
Step 1) We start by finding the first (F) and last (L) odd numbers from 3 to 21. It is easy to do that by simply looking at the numbers. The first odd number is 3, and the last odd number is 21.
F = 3
L = 21
Step 2) Next, we calculate the total odd numbers (T) there are from 3 to 21, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (21 - 3 + 2) ÷ 2
T = 20 ÷ 2
T = 10
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 21, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (10 ÷ 2) × (2 × 3 + (2 × (10 - 1))
Sum = 5 × (6 + 18)
Sum = 5 × 24
Sum = 120
Sum of odd numbers from 3 to 21 = 120
Sum of Odd Numbers Calculator
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