What is the average of odd numbers from 1 to 129? Here we will show you how to calculate the average of odd numbers from 1 to 129.
To find the average of the odd numbers from 1 to 129, we first calculate how many odd numbers there are from 1 to 129. Then, we calculate the sum of odd numbers from 1 to 129. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 1 to 129, and the odd numbers within that range are from 1 to 129. Therefore, the first odd number in the sequence is 1, and the last odd number in the sequence is 129.
Step 1) Calculate the total number of odd numbers from 1 to 129
Here we calculate the total number of odd numbers from 1 to 129 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 = (129 - 1 + 2) ÷ 2
tot = 130 ÷ 2
tot = 65
Total odd numbers from 1 to 129 = 65
Step 2) Calculate the sum of odd numbers from 1 to 129
To calculate the sum of odd numbers from 1 to 129, 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 × 1 + (2 × (65 - 1))
sum = 32.5 × (2 + 128)
sum = 32.5 × 130
sum = 4225
Sum of odd numbers from 1 to 129 = 4225
Step 3) Calculate the average of odd numbers from 1 to 129
Almost done! Now we can calculate the average of odd numbers from 1 to 129 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 = 4225 ÷ 65
Average = 65
Average of odd numbers from 1 to 129 = 65
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.