Answer:
[tex]S_{n}=10,455[/tex]
Step-by-step explanation:
find [tex]a_{30}[/tex]:
[tex]a_{n}=a_{1}+(n-1)d\\a_{30}=537+(30-1)(-13)\\a_{30}=537+(29)(-13)\\a_{30}=537+(-377)\\a_{30}= 160[/tex]
Solution:
[tex]S_{n}=\frac{n}{2} (a_{1}+a_{n})\\S_{n}=\frac{30}{2} (537+160)\\S_{n}=\frac{30}{2} (697)\\S_{n}=15(697)\\S_{n}=10,455[/tex]
