What is the average of even numbers from 1 to 152? Here we will show you how to calculate the average of even numbers from 1 to 152.
To find the average of the even numbers from 1 to 152, we first calculate how many even numbers there are from 1 to 152. Then, we calculate the sum of even numbers from 1 to 152. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 1 to 152, and the even numbers within that range are from 2 to 152. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 152.
Step 1) Calculate the total number of even numbers from 1 to 152
Here we calculate the total number of even numbers from 1 to 152 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 = (152 - 2 + 2) ÷ 2
tot = 152 ÷ 2
tot = 76
Total even numbers from 1 to 152 = 76
Step 2) Calculate the sum of even numbers from 1 to 152
To calculate the sum of even numbers from 1 to 152, 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 = (76 ÷ 2) × (2 × 2 + (2 × (76 - 1))
sum = 38 × (4 + 150)
sum = 38 × 154
sum = 5852
Sum of even numbers from 1 to 152 = 5852
Step 3) Calculate the average of even numbers from 1 to 152
Almost done! Now we can calculate the average of even numbers from 1 to 152 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 = 5852 ÷ 76
Average = 77
Average of even numbers from 1 to 152 = 77
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.