What is the average of even numbers from 1 to 1687? Here we will show you how to calculate the average of even numbers from 1 to 1687.
To find the average of the even numbers from 1 to 1687, we first calculate how many even numbers there are from 1 to 1687. Then, we calculate the sum of even numbers from 1 to 1687. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 1 to 1687, and the even numbers within that range are from 2 to 1686. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 1686.
Step 1) Calculate the total number of even numbers from 1 to 1687
Here we calculate the total number of even numbers from 1 to 1687 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 = (1686 - 2 + 2) ÷ 2
tot = 1686 ÷ 2
tot = 843
Total even numbers from 1 to 1687 = 843
Step 2) Calculate the sum of even numbers from 1 to 1687
To calculate the sum of even numbers from 1 to 1687, 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 = (843 ÷ 2) × (2 × 2 + (2 × (843 - 1))
sum = 421.5 × (4 + 1684)
sum = 421.5 × 1688
sum = 711492
Sum of even numbers from 1 to 1687 = 711492
Step 3) Calculate the average of even numbers from 1 to 1687
Almost done! Now we can calculate the average of even numbers from 1 to 1687 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 = 711492 ÷ 843
Average = 844
Average of even numbers from 1 to 1687 = 844
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.