What is the average of odd numbers from 100 to 121? Here we will show you how to calculate the average of odd numbers from 100 to 121.
To find the average of the odd numbers from 100 to 121, we first calculate how many odd numbers there are from 100 to 121. Then, we calculate the sum of odd numbers from 100 to 121. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 100 to 121, and the odd numbers within that range are from 101 to 121. Therefore, the first odd number in the sequence is 101, and the last odd number in the sequence is 121.
Step 1) Calculate the total number of odd numbers from 100 to 121
Here we calculate the total number of odd numbers from 100 to 121 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 = (121 - 101 + 2) ÷ 2
tot = 22 ÷ 2
tot = 11
Total odd numbers from 100 to 121 = 11
Step 2) Calculate the sum of odd numbers from 100 to 121
To calculate the sum of odd numbers from 100 to 121, 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 = (11 ÷ 2) × (2 × 101 + (2 × (11 - 1))
sum = 5.5 × (202 + 20)
sum = 5.5 × 222
sum = 1221
Sum of odd numbers from 100 to 121 = 1221
Step 3) Calculate the average of odd numbers from 100 to 121
Almost done! Now we can calculate the average of odd numbers from 100 to 121 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 = 1221 ÷ 11
Average = 111
Average of odd numbers from 100 to 121 = 111
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.