What is the average of odd numbers from 2 to 110? Here we will show you how to calculate the average of odd numbers from 2 to 110.
To find the average of the odd numbers from 2 to 110, we first calculate how many odd numbers there are from 2 to 110. Then, we calculate the sum of odd numbers from 2 to 110. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 2 to 110, and the odd numbers within that range are from 3 to 109. Therefore, the first odd number in the sequence is 3, and the last odd number in the sequence is 109.
Step 1) Calculate the total number of odd numbers from 2 to 110
Here we calculate the total number of odd numbers from 2 to 110 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 = (109 - 3 + 2) ÷ 2
tot = 108 ÷ 2
tot = 54
Total odd numbers from 2 to 110 = 54
Step 2) Calculate the sum of odd numbers from 2 to 110
To calculate the sum of odd numbers from 2 to 110, 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 = (54 ÷ 2) × (2 × 3 + (2 × (54 - 1))
sum = 27 × (6 + 106)
sum = 27 × 112
sum = 3024
Sum of odd numbers from 2 to 110 = 3024
Step 3) Calculate the average of odd numbers from 2 to 110
Almost done! Now we can calculate the average of odd numbers from 2 to 110 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 = 3024 ÷ 54
Average = 56
Average of odd numbers from 2 to 110 = 56
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.