What is the average of odd numbers from 100 to 159? Here we will show you how to calculate the average of odd numbers from 100 to 159.
To find the average of the odd numbers from 100 to 159, we first calculate how many odd numbers there are from 100 to 159. Then, we calculate the sum of odd numbers from 100 to 159. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 100 to 159, and the odd numbers within that range are from 101 to 159. Therefore, the first odd number in the sequence is 101, and the last odd number in the sequence is 159.
Step 1) Calculate the total number of odd numbers from 100 to 159
Here we calculate the total number of odd numbers from 100 to 159 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 = (159 - 101 + 2) ÷ 2
tot = 60 ÷ 2
tot = 30
Total odd numbers from 100 to 159 = 30
Step 2) Calculate the sum of odd numbers from 100 to 159
To calculate the sum of odd numbers from 100 to 159, 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 = (30 ÷ 2) × (2 × 101 + (2 × (30 - 1))
sum = 15 × (202 + 58)
sum = 15 × 260
sum = 3900
Sum of odd numbers from 100 to 159 = 3900
Step 3) Calculate the average of odd numbers from 100 to 159
Almost done! Now we can calculate the average of odd numbers from 100 to 159 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 = 3900 ÷ 30
Average = 130
Average of odd numbers from 100 to 159 = 130
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.