What is the average of even numbers from 1 to 1480? Here we will show you how to calculate the average of even numbers from 1 to 1480.
To find the average of the even numbers from 1 to 1480, we first calculate how many even numbers there are from 1 to 1480. Then, we calculate the sum of even numbers from 1 to 1480. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 1 to 1480, and the even numbers within that range are from 2 to 1480. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 1480.
Step 1) Calculate the total number of even numbers from 1 to 1480
Here we calculate the total number of even numbers from 1 to 1480 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 = (1480 - 2 + 2) ÷ 2
tot = 1480 ÷ 2
tot = 740
Total even numbers from 1 to 1480 = 740
Step 2) Calculate the sum of even numbers from 1 to 1480
To calculate the sum of even numbers from 1 to 1480, 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 = (740 ÷ 2) × (2 × 2 + (2 × (740 - 1))
sum = 370 × (4 + 1478)
sum = 370 × 1482
sum = 548340
Sum of even numbers from 1 to 1480 = 548340
Step 3) Calculate the average of even numbers from 1 to 1480
Almost done! Now we can calculate the average of even numbers from 1 to 1480 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 = 548340 ÷ 740
Average = 741
Average of even numbers from 1 to 1480 = 741
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.