What is the average of even numbers from 21 to 117? Here we will show you how to calculate the average of even numbers from 21 to 117.
To find the average of the even numbers from 21 to 117, we first calculate how many even numbers there are from 21 to 117. Then, we calculate the sum of even numbers from 21 to 117. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 21 to 117, and the even numbers within that range are from 22 to 116. Therefore, the first even number in the sequence is 22, and the last even number in the sequence is 116.
Step 1) Calculate the total number of even numbers from 21 to 117
Here we calculate the total number of even numbers from 21 to 117 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 = (116 - 22 + 2) ÷ 2
tot = 96 ÷ 2
tot = 48
Total even numbers from 21 to 117 = 48
Step 2) Calculate the sum of even numbers from 21 to 117
To calculate the sum of even numbers from 21 to 117, 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 = (48 ÷ 2) × (2 × 22 + (2 × (48 - 1))
sum = 24 × (44 + 94)
sum = 24 × 138
sum = 3312
Sum of even numbers from 21 to 117 = 3312
Step 3) Calculate the average of even numbers from 21 to 117
Almost done! Now we can calculate the average of even numbers from 21 to 117 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 = 3312 ÷ 48
Average = 69
Average of even numbers from 21 to 117 = 69
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.