Answer:
[tex]S_{n}=117[/tex]
Step-by-step explanation:
find [tex]a_{13}[/tex] first:
[tex]a_{n}=a_{1}+(n-1)d\\a_{13}=-3+(13-1)2\\a_{13}=-3+(12)2\\a_{13}=-3+24\\a_{13}=21[/tex]
Solution:
[tex]S_{n}=\frac{n}{2}(a_{1}+a_{n})\\S_{n} =\frac{13}{2} (-3+21)\\S_{n}=\frac{13}{2} (18)\\S_{n}=6.5(18)\\S_{n}=117[/tex]
yung question sa comments:
[tex]a_{n}=a_{1}+(n-1)d\\a_{15}=10+(15-1)5\\a_{15}=10+(14)5\\a_{15}=10+70\\a_{15}=80[/tex]
[tex]S_{n}=\frac{n}{2}(a_{1}+a_{n})\\S_{n} =\frac{15}{2} (10+80)\\S_{n}=\frac{15}{2} (90)\\S_{n}=7.5(90)\\S_{n}=675[/tex]
[tex]a_{n}=a_{1}+(n-1)d\\a_{11}=-4+(11-1)7\\a_{11}=-4+(10)7\\a_{11}=-4+70\\a_{11}=66[/tex]
[tex]S_{n}=\frac{n}{2}(a_{1}+a_{n})\\S_{n} =\frac{11}{2} (-4+66)\\S_{n}=\frac{11}{2} (62)\\S_{n}=5.5(62)\\S_{n}=341[/tex]
