Question

What is the pattern in the sequence, `28, -2, -32, -62`?

Answer 1

So 'the pattern' is: "Subtract 30 from the previous number"

Explanation:

The first thing to try is to see if this is an Arithmetic sequence.

Suppose we had:
`n_1=28color(white)(....)-> 1st" position"`
`n_2=-2color(white)(.)->2nd" position"`
`n_3=-32->3rd" position"`
`n_4=-62->4th" position"`

`n_2-n_1=-2-28=-30`
`n_3-n_2=-32-(-2)=-30`
`n_4-n_3=-62-(-32)=-30`

The consistent difference demonstrates that this is an Arithmetic Sequence

`color(magenta)("So 'the pattern' is: Subtract 30 from the previous number")`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Using algebra to represent this")`

So if `n_i` represents the value in position `i`:

`color(blue)(n_i=n_(i-1)-30)` where `n_(i-1)` represents the value in the previous position