Question

The sum of the first 100 positive whole numbers is 5050. What is the sum of the first 100 positive odd whole number?

Answer 1

The series of odd numbers is:

1, 3, 5, 7, 9, 11, 13, ....

If you observe this series, it is an Arithmetic Series with first term as 1 and common difference of 2. Common difference is defined as the difference between two consecutive terms of the series. So by using the formula of sum of an Arithmetic Series, we can find the sum of first 100 positive odd whole numbers.

The formula for the sum of an Arithmetic Series is:

$S_{n}=\frac{n}{2}(2a_{1}+(n-1)*d)$

Here,

n = number of terms = 100

a₁ = first term = 1

d = Common Difference = 2

Using the values, we get:

$S_{100}=\frac{100}{2}(2(1)+99*2)\\ \\ S_{100}=10000$

Thus, the sum of first 100 positive odd whole numbers is 10,000.