What is the average of even numbers from 144 to 180? Here we will show you how to calculate the average of even numbers from 144 to 180.
To find the average of the even numbers from 144 to 180, we first calculate how many even numbers there are from 144 to 180. Then, we calculate the sum of even numbers from 144 to 180. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 144 to 180, and the even numbers within that range are from 144 to 180. Therefore, the first even number in the sequence is 144, and the last even number in the sequence is 180.
Step 1) Calculate the total number of even numbers from 144 to 180
Here we calculate the total number of even numbers from 144 to 180 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 = (180 - 144 + 2) ÷ 2
tot = 38 ÷ 2
tot = 19
Total even numbers from 144 to 180 = 19
Step 2) Calculate the sum of even numbers from 144 to 180
To calculate the sum of even numbers from 144 to 180, 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 = (19 ÷ 2) × (2 × 144 + (2 × (19 - 1))
sum = 9.5 × (288 + 36)
sum = 9.5 × 324
sum = 3078
Sum of even numbers from 144 to 180 = 3078
Step 3) Calculate the average of even numbers from 144 to 180
Almost done! Now we can calculate the average of even numbers from 144 to 180 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 = 3078 ÷ 19
Average = 162
Average of even numbers from 144 to 180 = 162
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.