What is the average of even numbers from 1 to 1605? Here we will show you how to calculate the average of even numbers from 1 to 1605.
To find the average of the even numbers from 1 to 1605, we first calculate how many even numbers there are from 1 to 1605. Then, we calculate the sum of even numbers from 1 to 1605. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 1 to 1605, and the even numbers within that range are from 2 to 1604. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 1604.
Step 1) Calculate the total number of even numbers from 1 to 1605
Here we calculate the total number of even numbers from 1 to 1605 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 = (1604 - 2 + 2) ÷ 2
tot = 1604 ÷ 2
tot = 802
Total even numbers from 1 to 1605 = 802
Step 2) Calculate the sum of even numbers from 1 to 1605
To calculate the sum of even numbers from 1 to 1605, 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 = (802 ÷ 2) × (2 × 2 + (2 × (802 - 1))
sum = 401 × (4 + 1602)
sum = 401 × 1606
sum = 644006
Sum of even numbers from 1 to 1605 = 644006
Step 3) Calculate the average of even numbers from 1 to 1605
Almost done! Now we can calculate the average of even numbers from 1 to 1605 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 = 644006 ÷ 802
Average = 803
Average of even numbers from 1 to 1605 = 803
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.