What is the average of even numbers from 21 to 138? Here we will show you how to calculate the average of even numbers from 21 to 138.
To find the average of the even numbers from 21 to 138, we first calculate how many even numbers there are from 21 to 138. Then, we calculate the sum of even numbers from 21 to 138. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 21 to 138, and the even numbers within that range are from 22 to 138. Therefore, the first even number in the sequence is 22, and the last even number in the sequence is 138.
Step 1) Calculate the total number of even numbers from 21 to 138
Here we calculate the total number of even numbers from 21 to 138 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 = (138 - 22 + 2) ÷ 2
tot = 118 ÷ 2
tot = 59
Total even numbers from 21 to 138 = 59
Step 2) Calculate the sum of even numbers from 21 to 138
To calculate the sum of even numbers from 21 to 138, 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 = (59 ÷ 2) × (2 × 22 + (2 × (59 - 1))
sum = 29.5 × (44 + 116)
sum = 29.5 × 160
sum = 4720
Sum of even numbers from 21 to 138 = 4720
Step 3) Calculate the average of even numbers from 21 to 138
Almost done! Now we can calculate the average of even numbers from 21 to 138 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 = 4720 ÷ 59
Average = 80
Average of even numbers from 21 to 138 = 80
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.