Answer:
127.5
Step-by-step explanation:
The given series is 26 + 24.5 + 23 + 21.5 + ... - 17.5
The first term of this series is a=26
The common difference is d=24.5-26=-1.5
The last term of the series is -17.5
The nth term is given by:
[tex]u_n=a+d(n-1)[/tex]
[tex]26+-1.5(n-1)=-17.5[/tex]
[tex]-1.5n=-17.5-26-1.5[/tex]
[tex]-1.5n=-45[/tex]
n=30
The sum of the series:
[tex]S_{n}=\frac{n}{2}(a+l)[/tex]
[tex]S_{30}=\frac{30}{2}(26+-17.5)[/tex]
[tex]S_{30}=127.5[/tex]
