What is the average of even numbers from 101 to 120? Here we will show you how to calculate the average of even numbers from 101 to 120.
To find the average of the even numbers from 101 to 120, we first calculate how many even numbers there are from 101 to 120. Then, we calculate the sum of even numbers from 101 to 120. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 101 to 120, and the even numbers within that range are from 102 to 120. Therefore, the first even number in the sequence is 102, and the last even number in the sequence is 120.
Step 1) Calculate the total number of even numbers from 101 to 120
Here we calculate the total number of even numbers from 101 to 120 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 = (120 - 102 + 2) ÷ 2
tot = 20 ÷ 2
tot = 10
Total even numbers from 101 to 120 = 10
Step 2) Calculate the sum of even numbers from 101 to 120
To calculate the sum of even numbers from 101 to 120, 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 = (10 ÷ 2) × (2 × 102 + (2 × (10 - 1))
sum = 5 × (204 + 18)
sum = 5 × 222
sum = 1110
Sum of even numbers from 101 to 120 = 1110
Step 3) Calculate the average of even numbers from 101 to 120
Almost done! Now we can calculate the average of even numbers from 101 to 120 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 = 1110 ÷ 10
Average = 111
Average of even numbers from 101 to 120 = 111
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.