What is the average of even numbers from 21 to 137? Here we will show you how to calculate the average of even numbers from 21 to 137.
To find the average of the even numbers from 21 to 137, we first calculate how many even numbers there are from 21 to 137. Then, we calculate the sum of even numbers from 21 to 137. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 21 to 137, and the even numbers within that range are from 22 to 136. Therefore, the first even number in the sequence is 22, and the last even number in the sequence is 136.
Step 1) Calculate the total number of even numbers from 21 to 137
Here we calculate the total number of even numbers from 21 to 137 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 = (136 - 22 + 2) ÷ 2
tot = 116 ÷ 2
tot = 58
Total even numbers from 21 to 137 = 58
Step 2) Calculate the sum of even numbers from 21 to 137
To calculate the sum of even numbers from 21 to 137, 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 = (58 ÷ 2) × (2 × 22 + (2 × (58 - 1))
sum = 29 × (44 + 114)
sum = 29 × 158
sum = 4582
Sum of even numbers from 21 to 137 = 4582
Step 3) Calculate the average of even numbers from 21 to 137
Almost done! Now we can calculate the average of even numbers from 21 to 137 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 = 4582 ÷ 58
Average = 79
Average of even numbers from 21 to 137 = 79
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.