What is the sum of odd numbers from 18 to 178? Here we will show you step-by-step how to calculate the sum of odd numbers from 18 to 178.
Step 1) We start by finding the first (F) and last (L) odd numbers from 18 to 178. It is easy to do that by simply looking at the numbers. The first odd number is 19, and the last odd number is 177.
F = 19
L = 177
Step 2) Next, we calculate the total odd numbers (T) there are from 18 to 178, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (177 - 19 + 2) ÷ 2
T = 160 ÷ 2
T = 80
Step 3) Finally, we use the information from Step 1 and Step 2, and another formula, to calculate the sum of odd numbers from 18 to 178, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (80 ÷ 2) × (2 × 19 + (2 × (80 - 1))
Sum = 40 × (38 + 158)
Sum = 40 × 196
Sum = 7840
Sum of odd numbers from 18 to 178 = 7840
Sum of Odd Numbers Calculator
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