What is the average of even numbers from 21 to 129? Here we will show you how to calculate the average of even numbers from 21 to 129.
To find the average of the even numbers from 21 to 129, we first calculate how many even numbers there are from 21 to 129. Then, we calculate the sum of even numbers from 21 to 129. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 21 to 129, and the even numbers within that range are from 22 to 128. Therefore, the first even number in the sequence is 22, and the last even number in the sequence is 128.
Step 1) Calculate the total number of even numbers from 21 to 129
Here we calculate the total number of even numbers from 21 to 129 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 = (128 - 22 + 2) ÷ 2
tot = 108 ÷ 2
tot = 54
Total even numbers from 21 to 129 = 54
Step 2) Calculate the sum of even numbers from 21 to 129
To calculate the sum of even numbers from 21 to 129, 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 = (54 ÷ 2) × (2 × 22 + (2 × (54 - 1))
sum = 27 × (44 + 106)
sum = 27 × 150
sum = 4050
Sum of even numbers from 21 to 129 = 4050
Step 3) Calculate the average of even numbers from 21 to 129
Almost done! Now we can calculate the average of even numbers from 21 to 129 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 = 4050 ÷ 54
Average = 75
Average of even numbers from 21 to 129 = 75
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.