What is the average of even numbers from 1 to 1940? Here we will show you how to calculate the average of even numbers from 1 to 1940.
To find the average of the even numbers from 1 to 1940, we first calculate how many even numbers there are from 1 to 1940. Then, we calculate the sum of even numbers from 1 to 1940. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 1 to 1940, and the even numbers within that range are from 2 to 1940. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 1940.
Step 1) Calculate the total number of even numbers from 1 to 1940
Here we calculate the total number of even numbers from 1 to 1940 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 = (1940 - 2 + 2) ÷ 2
tot = 1940 ÷ 2
tot = 970
Total even numbers from 1 to 1940 = 970
Step 2) Calculate the sum of even numbers from 1 to 1940
To calculate the sum of even numbers from 1 to 1940, 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 = (970 ÷ 2) × (2 × 2 + (2 × (970 - 1))
sum = 485 × (4 + 1938)
sum = 485 × 1942
sum = 941870
Sum of even numbers from 1 to 1940 = 941870
Step 3) Calculate the average of even numbers from 1 to 1940
Almost done! Now we can calculate the average of even numbers from 1 to 1940 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 = 941870 ÷ 970
Average = 971
Average of even numbers from 1 to 1940 = 971
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.