What is the average of even numbers from 100 to 142? Here we will show you how to calculate the average of even numbers from 100 to 142.
To find the average of the even numbers from 100 to 142, we first calculate how many even numbers there are from 100 to 142. Then, we calculate the sum of even numbers from 100 to 142. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 100 to 142, and the even numbers within that range are from 100 to 142. Therefore, the first even number in the sequence is 100, and the last even number in the sequence is 142.
Step 1) Calculate the total number of even numbers from 100 to 142
Here we calculate the total number of even numbers from 100 to 142 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 = (142 - 100 + 2) ÷ 2
tot = 44 ÷ 2
tot = 22
Total even numbers from 100 to 142 = 22
Step 2) Calculate the sum of even numbers from 100 to 142
To calculate the sum of even numbers from 100 to 142, 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 = (22 ÷ 2) × (2 × 100 + (2 × (22 - 1))
sum = 11 × (200 + 42)
sum = 11 × 242
sum = 2662
Sum of even numbers from 100 to 142 = 2662
Step 3) Calculate the average of even numbers from 100 to 142
Almost done! Now we can calculate the average of even numbers from 100 to 142 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 = 2662 ÷ 22
Average = 121
Average of even numbers from 100 to 142 = 121
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.