What is the sum of odd numbers from 6 to 90? Here we will show you step-by-step how to calculate the sum of odd numbers from 6 to 90.
Step 1) We start by finding the first (F) and last (L) odd numbers from 6 to 90. It is easy to do that by simply looking at the numbers. The first odd number is 7, and the last odd number is 89.
F = 7
L = 89
Step 2) Next, we calculate the total odd numbers (T) there are from 6 to 90, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (89 - 7 + 2) ÷ 2
T = 84 ÷ 2
T = 42
Step 3) Finally, we use the information from Step 1 and Step 2, and another formula, to calculate the sum of odd numbers from 6 to 90, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (42 ÷ 2) × (2 × 7 + (2 × (42 - 1))
Sum = 21 × (14 + 82)
Sum = 21 × 96
Sum = 2016
Sum of odd numbers from 6 to 90 = 2016
Sum of Odd Numbers Calculator
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