This is an arithmetic sequence.
[tex]S_n= \frac{(a_n+a_1)n}{2} [/tex]
But on these type of arithmetic sequences where you add all the numbers from 1 up to a certain number the formula is:
[tex]S_n=\frac{n(n+1) }{2} [/tex]
So the sum is:
[tex]S_{10,000}= \frac{10,000(10,001)}{2} =5,000*10,001=50,005,000[/tex]
