Answer:
output = -3n +1
Explanation:
Given an input/output table for a linear function, you want an expression for the output when the input is n.
Arithmetic sequence
The input values count up from 1, so we can consider the output values to be the terms of an arithmetic sequence.
The first term of the sequence is a1 = -2 (when n=1).
The common difference of the sequence is d = (-5 -(-2)) = -3.
The general (n-th) term of an arithmetic sequence is given by the formula ...
an = a1 +d(n -1)
For the known values of a1 and d, we find the n-th term to be ...
an = -2 +(-3)(n -1)
an = -2 -3n +3 . . . . . . . eliminate parentheses
an = -3n +1 . . . . . . . . collect terms
The term corresponding to an input value of n is ...
-3n +1