Explanation:
To find the sum of the arithmetic sequence \(10, 20, 30, \ldots, 1000\), follow these steps:

1. Identify the first term (\(a\)) and the common difference (\(d\)):

- First term \(a = 10\)
- Common difference \(d = 20 - 10 = 10\)

2. Find the number of terms (\(n\)):

The general term of the arithmetic sequence is given by:

\[
a_n = a + (n - 1)d
\]

Set \(a_n = 1000\):

\[
1000 = 10 + (n - 1) \times 10
\]

\[
1000 = 10 + 10(n - 1)
\]

\[
1000 = 10 + 10n - 10
\]

\[
1000 = 10n
\]

\[
n = \frac{1000}{10} = 100
\]

So, there are 100 terms in the sequence.

3. Calculate the sum of the sequence:

The sum \(S_n\) of the first \(n\) terms of an arithmetic sequence is given by:

\[
S_n = \frac{n}{2} \times (a + l)
\]

where \(l\) is the last term. Here, \(l = 1000\), \(a = 10\), and \(n = 100\):

\[
S_{100} = \frac{100}{2} \times (10 + 1000)
\]

\[
S_{100} = 50 \times 1010
\]

\[
S_{100} = 50,500
\]

Thus, the sum of the sequence is:

C. 50,500