Question

Find the missing term of the following sequence.

. . . –45, __, –12, . . .

–28.5

–21

–19.5

–33

Answer 1

The series is as follows:


`a_(n) = \{...,-45, a_(k),-12...\}`

So, we will analyze each term:

1. If
`a_(k)=-28.5` then:


`-28.5-(-45)=(33)/(2)`

`-12-(-28.5)=(33)/(2)`

2. If
`a_(k)=-21` then:


`-21-(-45)=24`

`-12-(-21)=9`

3. If
`a_(k)=-19.5` then:


`-19.5-(-45)=(51)/(2)`

`-12-(-19.5)=(5)/(2)`

3. If
`a_(k)=-33` then:


`-33-(-45)=12`

`-12-(-33)=21`

Finally, the sequence occurs when
`a_(k)=-28.5`
This is the missing term