What is the average of even numbers from 21 to 121? Here we will show you how to calculate the average of even numbers from 21 to 121.
To find the average of the even numbers from 21 to 121, we first calculate how many even numbers there are from 21 to 121. Then, we calculate the sum of even numbers from 21 to 121. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 21 to 121, and the even numbers within that range are from 22 to 120. Therefore, the first even number in the sequence is 22, and the last even number in the sequence is 120.
Step 1) Calculate the total number of even numbers from 21 to 121
Here we calculate the total number of even numbers from 21 to 121 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 = (120 - 22 + 2) ÷ 2
tot = 100 ÷ 2
tot = 50
Total even numbers from 21 to 121 = 50
Step 2) Calculate the sum of even numbers from 21 to 121
To calculate the sum of even numbers from 21 to 121, 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 = (50 ÷ 2) × (2 × 22 + (2 × (50 - 1))
sum = 25 × (44 + 98)
sum = 25 × 142
sum = 3550
Sum of even numbers from 21 to 121 = 3550
Step 3) Calculate the average of even numbers from 21 to 121
Almost done! Now we can calculate the average of even numbers from 21 to 121 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 = 3550 ÷ 50
Average = 71
Average of even numbers from 21 to 121 = 71
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.