To find the sum of the arithmetic sequence $10,20,30,\dots ,1000$, 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