The picture is a little blurred, it seems that you want the sum of the first 6 terms.
You can see that the sequence starts with 2, and then you get the next term by changing the sign and multiplying by 5 (i.e. multiplying by -5). So, the terms are
[tex]a_1 = 2\\a_2 = -10\\a_3 = 50\\a_4 = -250\\a_5 = 1250\\a_6=-6250[/tex]
If you sum these values, you get
[tex]2-10+50-250+1250-6250=-5208[/tex]
