What is the average of even numbers from 21 to 100? Here we will show you how to calculate the average of even numbers from 21 to 100.
To find the average of the even numbers from 21 to 100, we first calculate how many even numbers there are from 21 to 100. Then, we calculate the sum of even numbers from 21 to 100. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 21 to 100, and the even numbers within that range are from 22 to 100. Therefore, the first even number in the sequence is 22, and the last even number in the sequence is 100.
Step 1) Calculate the total number of even numbers from 21 to 100
Here we calculate the total number of even numbers from 21 to 100 by entering the first and last even number in the sequence into our formula. Here is the formula and the math:
tot = (last - first + 2) ÷ 2
tot = (100 - 22 + 2) ÷ 2
tot = 80 ÷ 2
tot = 40
Total even numbers from 21 to 100 = 40
Step 2) Calculate the sum of even numbers from 21 to 100
To calculate the sum of even numbers from 21 to 100, you enter the total even numbers (tot) from Step 1 and the first even number in the sequence into our formula. Here is the formula and the math:
sum = (tot ÷ 2) × (2 × first + (2 × (tot - 1))
sum = (40 ÷ 2) × (2 × 22 + (2 × (40 - 1))
sum = 20 × (44 + 78)
sum = 20 × 122
sum = 2440
Sum of even numbers from 21 to 100 = 2440
Step 3) Calculate the average of even numbers from 21 to 100
Almost done! Now we can calculate the average of even numbers from 21 to 100 by dividing the sum of even numbers from Step 2 by the total even numbers from Step 1. Here is the formula, the math, and the answer:
Average = sum ÷ tot
Average = 2440 ÷ 40
Average = 61
Average of even numbers from 21 to 100 = 61
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.