What is the average of even numbers from 1 to 109? Here we will show you how to calculate the average of even numbers from 1 to 109.
To find the average of the even numbers from 1 to 109, we first calculate how many even numbers there are from 1 to 109. Then, we calculate the sum of even numbers from 1 to 109. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 1 to 109, and the even numbers within that range are from 2 to 108. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 108.
Step 1) Calculate the total number of even numbers from 1 to 109
Here we calculate the total number of even numbers from 1 to 109 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 = (108 - 2 + 2) ÷ 2
tot = 108 ÷ 2
tot = 54
Total even numbers from 1 to 109 = 54
Step 2) Calculate the sum of even numbers from 1 to 109
To calculate the sum of even numbers from 1 to 109, 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 = (54 ÷ 2) × (2 × 2 + (2 × (54 - 1))
sum = 27 × (4 + 106)
sum = 27 × 110
sum = 2970
Sum of even numbers from 1 to 109 = 2970
Step 3) Calculate the average of even numbers from 1 to 109
Almost done! Now we can calculate the average of even numbers from 1 to 109 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 = 2970 ÷ 54
Average = 55
Average of even numbers from 1 to 109 = 55
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.