What is the average of even numbers from 3 to 30? Here we will show you how to calculate the average of even numbers from 3 to 30.
To find the average of the even numbers from 3 to 30, we first calculate how many even numbers there are from 3 to 30. Then, we calculate the sum of even numbers from 3 to 30. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 3 to 30, and the even numbers within that range are from 4 to 30. Therefore, the first even number in the sequence is 4, and the last even number in the sequence is 30.
Step 1) Calculate the total number of even numbers from 3 to 30
Here we calculate the total number of even numbers from 3 to 30 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 = (30 - 4 + 2) ÷ 2
tot = 28 ÷ 2
tot = 14
Total even numbers from 3 to 30 = 14
Step 2) Calculate the sum of even numbers from 3 to 30
To calculate the sum of even numbers from 3 to 30, 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 = (14 ÷ 2) × (2 × 4 + (2 × (14 - 1))
sum = 7 × (8 + 26)
sum = 7 × 34
sum = 238
Sum of even numbers from 3 to 30 = 238
Step 3) Calculate the average of even numbers from 3 to 30
Almost done! Now we can calculate the average of even numbers from 3 to 30 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 = 238 ÷ 14
Average = 17
Average of even numbers from 3 to 30 = 17
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.