What is the average of odd numbers from 100 to 143? Here we will show you how to calculate the average of odd numbers from 100 to 143.
To find the average of the odd numbers from 100 to 143, we first calculate how many odd numbers there are from 100 to 143. Then, we calculate the sum of odd numbers from 100 to 143. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 100 to 143, and the odd numbers within that range are from 101 to 143. Therefore, the first odd number in the sequence is 101, and the last odd number in the sequence is 143.
Step 1) Calculate the total number of odd numbers from 100 to 143
Here we calculate the total number of odd numbers from 100 to 143 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 = (143 - 101 + 2) ÷ 2
tot = 44 ÷ 2
tot = 22
Total odd numbers from 100 to 143 = 22
Step 2) Calculate the sum of odd numbers from 100 to 143
To calculate the sum of odd numbers from 100 to 143, 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 = (22 ÷ 2) × (2 × 101 + (2 × (22 - 1))
sum = 11 × (202 + 42)
sum = 11 × 244
sum = 2684
Sum of odd numbers from 100 to 143 = 2684
Step 3) Calculate the average of odd numbers from 100 to 143
Almost done! Now we can calculate the average of odd numbers from 100 to 143 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 = 2684 ÷ 22
Average = 122
Average of odd numbers from 100 to 143 = 122
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.