Given:
[tex]\mleft\lbrace-6,-\frac{9}{2},-3,-\frac{3}{2},0,\ldots\mright\rbrace[/tex]
Given sequence is an Ap sequence
[tex]\begin{gathered} d=-\frac{9}{2}-(-6) \\ d=-\frac{9}{2}+6 \\ d=\frac{3}{2} \end{gathered}[/tex][tex]a=-6[/tex][tex]\begin{gathered} a_n=a+(n-1)d \\ a_n=-6+(n-1)(\frac{3}{2}) \end{gathered}[/tex][tex]\begin{gathered} a_{57}=-6+56(\frac{3}{2}) \\ a_{57}=-6+28(3) \\ a_{57}=-6+84 \\ a_{57}=78 \end{gathered}[/tex]
Option A is the final answer.
