What is the average of even numbers from 145 to 172? Here we will show you how to calculate the average of even numbers from 145 to 172.
To find the average of the even numbers from 145 to 172, we first calculate how many even numbers there are from 145 to 172. Then, we calculate the sum of even numbers from 145 to 172. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 145 to 172, and the even numbers within that range are from 146 to 172. Therefore, the first even number in the sequence is 146, and the last even number in the sequence is 172.
Step 1) Calculate the total number of even numbers from 145 to 172
Here we calculate the total number of even numbers from 145 to 172 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 - 146 + 2) ÷ 2
tot = 28 ÷ 2
tot = 14
Total even numbers from 145 to 172 = 14
Step 2) Calculate the sum of even numbers from 145 to 172
To calculate the sum of even numbers from 145 to 172, 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 = (14 ÷ 2) × (2 × 146 + (2 × (14 - 1))
sum = 7 × (292 + 26)
sum = 7 × 318
sum = 2226
Sum of even numbers from 145 to 172 = 2226
Step 3) Calculate the average of even numbers from 145 to 172
Almost done! Now we can calculate the average of even numbers from 145 to 172 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 = 2226 ÷ 14
Average = 159
Average of even numbers from 145 to 172 = 159
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.