What is the average of even numbers from 21 to 106? Here we will show you how to calculate the average of even numbers from 21 to 106.
To find the average of the even numbers from 21 to 106, we first calculate how many even numbers there are from 21 to 106. Then, we calculate the sum of even numbers from 21 to 106. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 21 to 106, and the even numbers within that range are from 22 to 106. Therefore, the first even number in the sequence is 22, and the last even number in the sequence is 106.
Step 1) Calculate the total number of even numbers from 21 to 106
Here we calculate the total number of even numbers from 21 to 106 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 = (106 - 22 + 2) ÷ 2
tot = 86 ÷ 2
tot = 43
Total even numbers from 21 to 106 = 43
Step 2) Calculate the sum of even numbers from 21 to 106
To calculate the sum of even numbers from 21 to 106, 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 = (43 ÷ 2) × (2 × 22 + (2 × (43 - 1))
sum = 21.5 × (44 + 84)
sum = 21.5 × 128
sum = 2752
Sum of even numbers from 21 to 106 = 2752
Step 3) Calculate the average of even numbers from 21 to 106
Almost done! Now we can calculate the average of even numbers from 21 to 106 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 = 2752 ÷ 43
Average = 64
Average of even numbers from 21 to 106 = 64
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.