What is the average of the first 50 positive even numbers?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 51
The first 50 positive even numbers are: 2, 4, 6, 8, 10, 12, ..., 98, 100.
To find the average, we need to add up all these numbers and then divide by the total number of numbers, which is 50.
We can simplify this calculation by noticing that each even number can be written as 2 times an integer starting from 1, that is, 2, 4, 6, 8, ..., 100 can be written as 2(1), 2(2), 2(3), 2(4), ..., 2(50).
So, we can find the sum of the first 50 positive even numbers by adding up the integers from 1 to 50, and multiplying the result by 2:
2(1 + 2 + 3 + ... + 50) = 2(1275) = 2550.
Then, we divide by 50 to find the average:
2550/50 = 51.
Therefore, the average of the first 50 positive even numbers is 51.