What is the average of odd numbers from 1 to 10000? Here we will show you how to calculate the average of odd numbers from 1 to 10000.
To find the average of the odd numbers from 1 to 10000, we first calculate how many odd numbers there are from 1 to 10000. Then, we calculate the sum of odd numbers from 1 to 10000. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 1 to 10000, and the odd numbers within that range are from 1 to 9999. Therefore, the first odd number in the sequence is 1, and the last odd number in the sequence is 9999.
Step 1) Calculate the total number of odd numbers from 1 to 10000
Here we calculate the total number of odd numbers from 1 to 10000 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 = (9999 - 1 + 2) ÷ 2
tot = 10000 ÷ 2
tot = 5000
Total odd numbers from 1 to 10000 = 5000
Step 2) Calculate the sum of odd numbers from 1 to 10000
To calculate the sum of odd numbers from 1 to 10000, 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 = (5000 ÷ 2) × (2 × 1 + (2 × (5000 - 1))
sum = 2500 × (2 + 9998)
sum = 2500 × 10000
sum = 25000000
Sum of odd numbers from 1 to 10000 = 25000000
Step 3) Calculate the average of odd numbers from 1 to 10000
Almost done! Now we can calculate the average of odd numbers from 1 to 10000 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 = 25000000 ÷ 5000
Average = 5000
Average of odd numbers from 1 to 10000 = 5000
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.