What is the average of even numbers from 3 to 21? Here we will show you how to calculate the average of even numbers from 3 to 21.
To find the average of the even numbers from 3 to 21, we first calculate how many even numbers there are from 3 to 21. Then, we calculate the sum of even numbers from 3 to 21. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 3 to 21, and the even numbers within that range are from 4 to 20. Therefore, the first even number in the sequence is 4, and the last even number in the sequence is 20.
Step 1) Calculate the total number of even numbers from 3 to 21
Here we calculate the total number of even numbers from 3 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 - 4 + 2) ÷ 2
tot = 18 ÷ 2
tot = 9
Total even numbers from 3 to 21 = 9
Step 2) Calculate the sum of even numbers from 3 to 21
To calculate the sum of even numbers from 3 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 = (9 ÷ 2) × (2 × 4 + (2 × (9 - 1))
sum = 4.5 × (8 + 16)
sum = 4.5 × 24
sum = 108
Sum of even numbers from 3 to 21 = 108
Step 3) Calculate the average of even numbers from 3 to 21
Almost done! Now we can calculate the average of even numbers from 3 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 = 108 ÷ 9
Average = 12
Average of even numbers from 3 to 21 = 12
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.