What is the average of odd numbers from 2 to 123? Here we will show you how to calculate the average of odd numbers from 2 to 123.
To find the average of the odd numbers from 2 to 123, we first calculate how many odd numbers there are from 2 to 123. Then, we calculate the sum of odd numbers from 2 to 123. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 2 to 123, and the odd numbers within that range are from 3 to 123. Therefore, the first odd number in the sequence is 3, and the last odd number in the sequence is 123.
Step 1) Calculate the total number of odd numbers from 2 to 123
Here we calculate the total number of odd numbers from 2 to 123 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 = (123 - 3 + 2) ÷ 2
tot = 122 ÷ 2
tot = 61
Total odd numbers from 2 to 123 = 61
Step 2) Calculate the sum of odd numbers from 2 to 123
To calculate the sum of odd numbers from 2 to 123, 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 = (61 ÷ 2) × (2 × 3 + (2 × (61 - 1))
sum = 30.5 × (6 + 120)
sum = 30.5 × 126
sum = 3843
Sum of odd numbers from 2 to 123 = 3843
Step 3) Calculate the average of odd numbers from 2 to 123
Almost done! Now we can calculate the average of odd numbers from 2 to 123 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 = 3843 ÷ 61
Average = 63
Average of odd numbers from 2 to 123 = 63
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.