What is the average of even numbers from 100 to 173? Here we will show you how to calculate the average of even numbers from 100 to 173.
To find the average of the even numbers from 100 to 173, we first calculate how many even numbers there are from 100 to 173. Then, we calculate the sum of even numbers from 100 to 173. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 100 to 173, and the even numbers within that range are from 100 to 172. Therefore, the first even number in the sequence is 100, and the last even number in the sequence is 172.
Step 1) Calculate the total number of even numbers from 100 to 173
Here we calculate the total number of even numbers from 100 to 173 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 = (172 - 100 + 2) ÷ 2
tot = 74 ÷ 2
tot = 37
Total even numbers from 100 to 173 = 37
Step 2) Calculate the sum of even numbers from 100 to 173
To calculate the sum of even numbers from 100 to 173, 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 = (37 ÷ 2) × (2 × 100 + (2 × (37 - 1))
sum = 18.5 × (200 + 72)
sum = 18.5 × 272
sum = 5032
Sum of even numbers from 100 to 173 = 5032
Step 3) Calculate the average of even numbers from 100 to 173
Almost done! Now we can calculate the average of even numbers from 100 to 173 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 = 5032 ÷ 37
Average = 136
Average of even numbers from 100 to 173 = 136
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.