What is the average of even numbers from 1 to 1333? Here we will show you how to calculate the average of even numbers from 1 to 1333.
To find the average of the even numbers from 1 to 1333, we first calculate how many even numbers there are from 1 to 1333. Then, we calculate the sum of even numbers from 1 to 1333. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 1 to 1333, and the even numbers within that range are from 2 to 1332. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 1332.
Step 1) Calculate the total number of even numbers from 1 to 1333
Here we calculate the total number of even numbers from 1 to 1333 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 = (1332 - 2 + 2) ÷ 2
tot = 1332 ÷ 2
tot = 666
Total even numbers from 1 to 1333 = 666
Step 2) Calculate the sum of even numbers from 1 to 1333
To calculate the sum of even numbers from 1 to 1333, 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 = (666 ÷ 2) × (2 × 2 + (2 × (666 - 1))
sum = 333 × (4 + 1330)
sum = 333 × 1334
sum = 444222
Sum of even numbers from 1 to 1333 = 444222
Step 3) Calculate the average of even numbers from 1 to 1333
Almost done! Now we can calculate the average of even numbers from 1 to 1333 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 = 444222 ÷ 666
Average = 667
Average of even numbers from 1 to 1333 = 667
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.