What is the average of even numbers from 20 to 90? Here we will show you how to calculate the average of even numbers from 20 to 90.
To find the average of the even numbers from 20 to 90, we first calculate how many even numbers there are from 20 to 90. Then, we calculate the sum of even numbers from 20 to 90. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 20 to 90, and the even numbers within that range are from 20 to 90. Therefore, the first even number in the sequence is 20, and the last even number in the sequence is 90.
Step 1) Calculate the total number of even numbers from 20 to 90
Here we calculate the total number of even numbers from 20 to 90 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 = (90 - 20 + 2) ÷ 2
tot = 72 ÷ 2
tot = 36
Total even numbers from 20 to 90 = 36
Step 2) Calculate the sum of even numbers from 20 to 90
To calculate the sum of even numbers from 20 to 90, 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 = (36 ÷ 2) × (2 × 20 + (2 × (36 - 1))
sum = 18 × (40 + 70)
sum = 18 × 110
sum = 1980
Sum of even numbers from 20 to 90 = 1980
Step 3) Calculate the average of even numbers from 20 to 90
Almost done! Now we can calculate the average of even numbers from 20 to 90 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 = 1980 ÷ 36
Average = 55
Average of even numbers from 20 to 90 = 55
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.