What is the average of even numbers from 2 to 21? Here we will show you how to calculate the average of even numbers from 2 to 21.
To find the average of the even numbers from 2 to 21, we first calculate how many even numbers there are from 2 to 21. Then, we calculate the sum of even numbers from 2 to 21. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 2 to 21, and the even numbers within that range are from 2 to 20. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 20.
Step 1) Calculate the total number of even numbers from 2 to 21
Here we calculate the total number of even numbers from 2 to 21 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 = (20 - 2 + 2) ÷ 2
tot = 20 ÷ 2
tot = 10
Total even numbers from 2 to 21 = 10
Step 2) Calculate the sum of even numbers from 2 to 21
To calculate the sum of even numbers from 2 to 21, 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 = (10 ÷ 2) × (2 × 2 + (2 × (10 - 1))
sum = 5 × (4 + 18)
sum = 5 × 22
sum = 110
Sum of even numbers from 2 to 21 = 110
Step 3) Calculate the average of even numbers from 2 to 21
Almost done! Now we can calculate the average of even numbers from 2 to 21 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 = 110 ÷ 10
Average = 11
Average of even numbers from 2 to 21 = 11
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.