What is the average of odd numbers from 100 to 145? Here we will show you how to calculate the average of odd numbers from 100 to 145.
To find the average of the odd numbers from 100 to 145, we first calculate how many odd numbers there are from 100 to 145. Then, we calculate the sum of odd numbers from 100 to 145. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 100 to 145, and the odd numbers within that range are from 101 to 145. Therefore, the first odd number in the sequence is 101, and the last odd number in the sequence is 145.
Step 1) Calculate the total number of odd numbers from 100 to 145
Here we calculate the total number of odd numbers from 100 to 145 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 = (145 - 101 + 2) ÷ 2
tot = 46 ÷ 2
tot = 23
Total odd numbers from 100 to 145 = 23
Step 2) Calculate the sum of odd numbers from 100 to 145
To calculate the sum of odd numbers from 100 to 145, 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 = (23 ÷ 2) × (2 × 101 + (2 × (23 - 1))
sum = 11.5 × (202 + 44)
sum = 11.5 × 246
sum = 2829
Sum of odd numbers from 100 to 145 = 2829
Step 3) Calculate the average of odd numbers from 100 to 145
Almost done! Now we can calculate the average of odd numbers from 100 to 145 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 = 2829 ÷ 23
Average = 123
Average of odd numbers from 100 to 145 = 123
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.