Answer:
[tex]S_{10}=-55[/tex]
Step-by-step explanation:
The given series is
[tex](-1)+(-2)+(-3)+...+(-10)[/tex]
The first term of this arithmetic sequence is
[tex]a_1=-1[/tex] the last term is [tex]l=-10[/tex]
The sum of the first n-terms is given by
[tex]S_n=\frac{n}{2}(a_1+l)[/tex]
The first 10 terms is
[tex]S_{10}=\frac{10}{2}(-1+-10)[/tex]
[tex]S_{10}=5(-11)[/tex]
[tex]S_{10}=-55[/tex]
