What is the average of even numbers from 101 to 112? Here we will show you how to calculate the average of even numbers from 101 to 112.
To find the average of the even numbers from 101 to 112, we first calculate how many even numbers there are from 101 to 112. Then, we calculate the sum of even numbers from 101 to 112. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 101 to 112, and the even numbers within that range are from 102 to 112. Therefore, the first even number in the sequence is 102, and the last even number in the sequence is 112.
Step 1) Calculate the total number of even numbers from 101 to 112
Here we calculate the total number of even numbers from 101 to 112 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 = (112 - 102 + 2) ÷ 2
tot = 12 ÷ 2
tot = 6
Total even numbers from 101 to 112 = 6
Step 2) Calculate the sum of even numbers from 101 to 112
To calculate the sum of even numbers from 101 to 112, 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 = (6 ÷ 2) × (2 × 102 + (2 × (6 - 1))
sum = 3 × (204 + 10)
sum = 3 × 214
sum = 642
Sum of even numbers from 101 to 112 = 642
Step 3) Calculate the average of even numbers from 101 to 112
Almost done! Now we can calculate the average of even numbers from 101 to 112 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 = 642 ÷ 6
Average = 107
Average of even numbers from 101 to 112 = 107
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.