The average of all the odd numbers up to 100 will be:

The correct answer is Option (1) → 50

The odd numbers up to 100 are 1, 3, 5, ..., 99. The sum of the first \(n\) odd numbers is \(n^2\), and the average is the sum divided by how many numbers there are.

• Number of odd numbers from 1 to 99 \(=50\)

• Their sum, the square of 50: \(50^2=2500\)

• Average, the sum divided by 50: \(\displaystyle \frac{2500}{50}=50\)

Shortcut: For numbers that go up in equal steps, the average is the average of the first and the last.

• Average of the first and the last odd numbers: \(\displaystyle \frac{1+99}{2}=50\)