ANSWER
The 4th term is -27
EXPLANATION
The sum of the first n-terms of an arithmetic sequence is
[tex]S_n= \frac{n}{2} (2a_1+d(n-1))[/tex]
It was given that,
[tex]S_4 = - 36[/tex]
[tex]a_1 = 9[/tex]
[tex] - 36= \frac{ 4}{2} (2 \times 9+d(4-1))[/tex]
[tex]-36=2(18+3d)[/tex]
[tex]-18=18+3d[/tex]
[tex]-18 - 18 = 3d[/tex]
[tex] 3d = - 36[/tex]
[tex]d = - 12[/tex]
The n-term is given by:
[tex]a_n=a_1+ (n-1)d[/tex]
We substitute n=4 to get,
[tex]a_4=9+ (4-1) \times -12[/tex]
[tex]a_4=9+ 3\times -12[/tex]
[tex]a_4=9 - 36[/tex]
[tex]a_4= - 27[/tex]
