What is the average of even numbers from 1 to 1369? Here we will show you how to calculate the average of even numbers from 1 to 1369.
To find the average of the even numbers from 1 to 1369, we first calculate how many even numbers there are from 1 to 1369. Then, we calculate the sum of even numbers from 1 to 1369. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 1 to 1369, and the even numbers within that range are from 2 to 1368. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 1368.
Step 1) Calculate the total number of even numbers from 1 to 1369
Here we calculate the total number of even numbers from 1 to 1369 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 = (1368 - 2 + 2) ÷ 2
tot = 1368 ÷ 2
tot = 684
Total even numbers from 1 to 1369 = 684
Step 2) Calculate the sum of even numbers from 1 to 1369
To calculate the sum of even numbers from 1 to 1369, 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 = (684 ÷ 2) × (2 × 2 + (2 × (684 - 1))
sum = 342 × (4 + 1366)
sum = 342 × 1370
sum = 468540
Sum of even numbers from 1 to 1369 = 468540
Step 3) Calculate the average of even numbers from 1 to 1369
Almost done! Now we can calculate the average of even numbers from 1 to 1369 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 = 468540 ÷ 684
Average = 685
Average of even numbers from 1 to 1369 = 685
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.