SOLUTION
The given sequence is
From the sequence it follows
[tex]a=8,d=-3[/tex]
The formula for sum of an arithmetic sequence
[tex]S=\frac{n}{2}(a+l)[/tex]
Since the number of terms is not given then
Using the nth term formula
[tex]a_n=a+(n-1)d[/tex]
Substitute
[tex]a_n=-403,a=8,d=-3[/tex]
Into the nth term formula
[tex]\begin{gathered} -403=8+(n-1)-3 \\ -403=8-3n+3 \\ -403-11=-3n \\ -3n=-414 \\ n=138 \end{gathered}[/tex]
Therefore the sum is
[tex]\begin{gathered} S=\frac{138}{2}(8+(-403)) \\ S=69(-395) \\ S=-27255 \end{gathered}[/tex]
Therefore the solution is:
[tex]S=-27255[/tex]
