What is the average of even numbers from 21 to 116? Here we will show you how to calculate the average of even numbers from 21 to 116.
To find the average of the even numbers from 21 to 116, we first calculate how many even numbers there are from 21 to 116. Then, we calculate the sum of even numbers from 21 to 116. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 21 to 116, 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 116
Here we calculate the total number of even numbers from 21 to 116 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 116 = 48
Step 2) Calculate the sum of even numbers from 21 to 116
To calculate the sum of even numbers from 21 to 116, 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 116 = 3312
Step 3) Calculate the average of even numbers from 21 to 116
Almost done! Now we can calculate the average of even numbers from 21 to 116 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 116 = 69
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.