What is the average of odd numbers from 1 to 3733? Here we will show you how to calculate the average of odd numbers from 1 to 3733.
To find the average of the odd numbers from 1 to 3733, we first calculate how many odd numbers there are from 1 to 3733. Then, we calculate the sum of odd numbers from 1 to 3733. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 1 to 3733, and the odd numbers within that range are from 1 to 3733. Therefore, the first odd number in the sequence is 1, and the last odd number in the sequence is 3733.
Step 1) Calculate the total number of odd numbers from 1 to 3733
Here we calculate the total number of odd numbers from 1 to 3733 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 = (3733 - 1 + 2) ÷ 2
tot = 3734 ÷ 2
tot = 1867
Total odd numbers from 1 to 3733 = 1867
Step 2) Calculate the sum of odd numbers from 1 to 3733
To calculate the sum of odd numbers from 1 to 3733, 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 = (1867 ÷ 2) × (2 × 1 + (2 × (1867 - 1))
sum = 933.5 × (2 + 3732)
sum = 933.5 × 3734
sum = 3485689
Sum of odd numbers from 1 to 3733 = 3485689
Step 3) Calculate the average of odd numbers from 1 to 3733
Almost done! Now we can calculate the average of odd numbers from 1 to 3733 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 = 3485689 ÷ 1867
Average = 1867
Average of odd numbers from 1 to 3733 = 1867
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.