What is the average of even numbers from 20 to 135? Here we will show you how to calculate the average of even numbers from 20 to 135.
To find the average of the even numbers from 20 to 135, we first calculate how many even numbers there are from 20 to 135. Then, we calculate the sum of even numbers from 20 to 135. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 20 to 135, and the even numbers within that range are from 20 to 134. Therefore, the first even number in the sequence is 20, and the last even number in the sequence is 134.
Step 1) Calculate the total number of even numbers from 20 to 135
Here we calculate the total number of even numbers from 20 to 135 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 = (134 - 20 + 2) ÷ 2
tot = 116 ÷ 2
tot = 58
Total even numbers from 20 to 135 = 58
Step 2) Calculate the sum of even numbers from 20 to 135
To calculate the sum of even numbers from 20 to 135, 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 = (58 ÷ 2) × (2 × 20 + (2 × (58 - 1))
sum = 29 × (40 + 114)
sum = 29 × 154
sum = 4466
Sum of even numbers from 20 to 135 = 4466
Step 3) Calculate the average of even numbers from 20 to 135
Almost done! Now we can calculate the average of even numbers from 20 to 135 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 = 4466 ÷ 58
Average = 77
Average of even numbers from 20 to 135 = 77
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.