The series is as follows:
[tex]a_{n} = \{...,-45, a_{k},-12...\}[/tex]
So, we will analyze each term:
1. If [tex]a_{k}=-28.5[/tex] then:
[tex]-28.5-(-45)=\frac{33}{2}[/tex]
[tex]-12-(-28.5)=\frac{33}{2}[/tex]
2. If [tex]a_{k}=-21[/tex] then:
[tex]-21-(-45)=24[/tex]
[tex]-12-(-21)=9[/tex]
3. If [tex]a_{k}=-19.5[/tex] then:
[tex]-19.5-(-45)=\frac{51}{2}[/tex]
[tex]-12-(-19.5)=\frac{5}{2}[/tex]
3. If [tex]a_{k}=-33[/tex] then:
[tex]-33-(-45)=12[/tex]
[tex]-12-(-33)=21[/tex]
Finally, the sequence occurs when [tex]a_{k}=-28.5[/tex]
This is the missing term
