What is the average of even numbers from 1 to 1600? Here we will show you how to calculate the average of even numbers from 1 to 1600.
To find the average of the even numbers from 1 to 1600, we first calculate how many even numbers there are from 1 to 1600. Then, we calculate the sum of even numbers from 1 to 1600. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 1 to 1600, and the even numbers within that range are from 2 to 1600. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 1600.
Step 1) Calculate the total number of even numbers from 1 to 1600
Here we calculate the total number of even numbers from 1 to 1600 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 = (1600 - 2 + 2) ÷ 2
tot = 1600 ÷ 2
tot = 800
Total even numbers from 1 to 1600 = 800
Step 2) Calculate the sum of even numbers from 1 to 1600
To calculate the sum of even numbers from 1 to 1600, 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 = (800 ÷ 2) × (2 × 2 + (2 × (800 - 1))
sum = 400 × (4 + 1598)
sum = 400 × 1602
sum = 640800
Sum of even numbers from 1 to 1600 = 640800
Step 3) Calculate the average of even numbers from 1 to 1600
Almost done! Now we can calculate the average of even numbers from 1 to 1600 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 = 640800 ÷ 800
Average = 801
Average of even numbers from 1 to 1600 = 801
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.