What is the sum of the first hundred odd numbers?

The first hundred odd numbers form an arithmetic progression: $1, 3, 5, \dots$.

We need the sum of the first hundred odd numbers, so the number of terms $n = 100$.
The first term $a_1 = 1$.

The $n$-th odd number is given by the formula $2n - 1$.
For the 100th odd number, $a_{100} = 2(100) - 1 = 200 - 1 = 199$.

The sum of an arithmetic progression is given by the formula $S_n = \frac{n}{2}(a_1 + a_n)$.
Substitute the values:

Alternatively, the sum of the first $n$ odd numbers is $n^2$.
For $n=100$:

The sum of the first hundred odd numbers is 10000.

Comparing this with the given options:
A 200
B 500
C 1 000
D 10 000
E 100 000

The correct option is D.

The final answer is $\boxed{\text{10 000}}$.