What is the average of odd numbers from 8 to 137? Here we will show you how to calculate the average of odd numbers from 8 to 137.
To find the average of the odd numbers from 8 to 137, we first calculate how many odd numbers there are from 8 to 137. Then, we calculate the sum of odd numbers from 8 to 137. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 8 to 137, and the odd numbers within that range are from 9 to 137. Therefore, the first odd number in the sequence is 9, and the last odd number in the sequence is 137.
Step 1) Calculate the total number of odd numbers from 8 to 137
Here we calculate the total number of odd numbers from 8 to 137 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 = (137 - 9 + 2) ÷ 2
tot = 130 ÷ 2
tot = 65
Total odd numbers from 8 to 137 = 65
Step 2) Calculate the sum of odd numbers from 8 to 137
To calculate the sum of odd numbers from 8 to 137, 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 = (65 ÷ 2) × (2 × 9 + (2 × (65 - 1))
sum = 32.5 × (18 + 128)
sum = 32.5 × 146
sum = 4745
Sum of odd numbers from 8 to 137 = 4745
Step 3) Calculate the average of odd numbers from 8 to 137
Almost done! Now we can calculate the average of odd numbers from 8 to 137 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 = 4745 ÷ 65
Average = 73
Average of odd numbers from 8 to 137 = 73
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.