What is the Nth term for this linear sequence: - 2,-2,-2,-2,-2?

The nth term is the difference between the numbers, followed by an addition/subtraction to 'correct' the values to what they are in the sequence.

The difference here is 0, so we have 0n so that means every number is 0 therefore we need to correct that to what it is:

Nth term = 0n-2

You've given us enough of the series to show clearly that the Nth term is - 2.