What is the average of even numbers from 21 to 105? Here we will show you how to calculate the average of even numbers from 21 to 105.
To find the average of the even numbers from 21 to 105, we first calculate how many even numbers there are from 21 to 105. Then, we calculate the sum of even numbers from 21 to 105. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 21 to 105, and the even numbers within that range are from 22 to 104. Therefore, the first even number in the sequence is 22, and the last even number in the sequence is 104.
Step 1) Calculate the total number of even numbers from 21 to 105
Here we calculate the total number of even numbers from 21 to 105 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 = (104 - 22 + 2) ÷ 2
tot = 84 ÷ 2
tot = 42
Total even numbers from 21 to 105 = 42
Step 2) Calculate the sum of even numbers from 21 to 105
To calculate the sum of even numbers from 21 to 105, 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 = (42 ÷ 2) × (2 × 22 + (2 × (42 - 1))
sum = 21 × (44 + 82)
sum = 21 × 126
sum = 2646
Sum of even numbers from 21 to 105 = 2646
Step 3) Calculate the average of even numbers from 21 to 105
Almost done! Now we can calculate the average of even numbers from 21 to 105 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 = 2646 ÷ 42
Average = 63
Average of even numbers from 21 to 105 = 63
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.