What is the average of even numbers from 10 to 171? Here we will show you how to calculate the average of even numbers from 10 to 171.
To find the average of the even numbers from 10 to 171, we first calculate how many even numbers there are from 10 to 171. Then, we calculate the sum of even numbers from 10 to 171. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 10 to 171, and the even numbers within that range are from 10 to 170. Therefore, the first even number in the sequence is 10, and the last even number in the sequence is 170.
Step 1) Calculate the total number of even numbers from 10 to 171
Here we calculate the total number of even numbers from 10 to 171 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 = (170 - 10 + 2) ÷ 2
tot = 162 ÷ 2
tot = 81
Total even numbers from 10 to 171 = 81
Step 2) Calculate the sum of even numbers from 10 to 171
To calculate the sum of even numbers from 10 to 171, 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 = (81 ÷ 2) × (2 × 10 + (2 × (81 - 1))
sum = 40.5 × (20 + 160)
sum = 40.5 × 180
sum = 7290
Sum of even numbers from 10 to 171 = 7290
Step 3) Calculate the average of even numbers from 10 to 171
Almost done! Now we can calculate the average of even numbers from 10 to 171 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 = 7290 ÷ 81
Average = 90
Average of even numbers from 10 to 171 = 90
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.