What is the average of odd numbers from 2 to 106? Here we will show you how to calculate the average of odd numbers from 2 to 106.
To find the average of the odd numbers from 2 to 106, we first calculate how many odd numbers there are from 2 to 106. Then, we calculate the sum of odd numbers from 2 to 106. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 2 to 106, and the odd numbers within that range are from 3 to 105. Therefore, the first odd number in the sequence is 3, and the last odd number in the sequence is 105.
Step 1) Calculate the total number of odd numbers from 2 to 106
Here we calculate the total number of odd numbers from 2 to 106 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 = (105 - 3 + 2) ÷ 2
tot = 104 ÷ 2
tot = 52
Total odd numbers from 2 to 106 = 52
Step 2) Calculate the sum of odd numbers from 2 to 106
To calculate the sum of odd numbers from 2 to 106, 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 = (52 ÷ 2) × (2 × 3 + (2 × (52 - 1))
sum = 26 × (6 + 102)
sum = 26 × 108
sum = 2808
Sum of odd numbers from 2 to 106 = 2808
Step 3) Calculate the average of odd numbers from 2 to 106
Almost done! Now we can calculate the average of odd numbers from 2 to 106 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 = 2808 ÷ 52
Average = 54
Average of odd numbers from 2 to 106 = 54
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.