What is the average of odd numbers from 100 to 120? Here we will show you how to calculate the average of odd numbers from 100 to 120.
To find the average of the odd numbers from 100 to 120, we first calculate how many odd numbers there are from 100 to 120. Then, we calculate the sum of odd numbers from 100 to 120. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 100 to 120, and the odd numbers within that range are from 101 to 119. Therefore, the first odd number in the sequence is 101, and the last odd number in the sequence is 119.
Step 1) Calculate the total number of odd numbers from 100 to 120
Here we calculate the total number of odd numbers from 100 to 120 by entering the first and last odd number in the sequence into our formula. Here is the formula and the math:
tot = (last - first + 2) ÷ 2
tot = (119 - 101 + 2) ÷ 2
tot = 20 ÷ 2
tot = 10
Total odd numbers from 100 to 120 = 10
Step 2) Calculate the sum of odd numbers from 100 to 120
To calculate the sum of odd numbers from 100 to 120, you enter the total odd numbers (tot) from Step 1 and the first odd number in the sequence into our formula. Here is the formula and the math:
sum = (tot ÷ 2) × (2 × first + (2 × (tot - 1))
sum = (10 ÷ 2) × (2 × 101 + (2 × (10 - 1))
sum = 5 × (202 + 18)
sum = 5 × 220
sum = 1100
Sum of odd numbers from 100 to 120 = 1100
Step 3) Calculate the average of odd numbers from 100 to 120
Almost done! Now we can calculate the average of odd numbers from 100 to 120 by dividing the sum of odd numbers from Step 2 by the total odd numbers from Step 1. Here is the formula, the math, and the answer:
Average = sum ÷ tot
Average = 1100 ÷ 10
Average = 110
Average of odd numbers from 100 to 120 = 110
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.