Answer
$$\eqalign{
& {a_n} = n - 3 \cr
& {\text{The domain is }}D:\left\{ {1,2,3,4,5,6} \right\} \cr
& {\text{The range is }}R:\left\{ { - 2, - 1,0,1,2,3} \right\} \cr} $$
Work Step by Step
$$\eqalign{
& {\text{From the graph we can see that}} \cr
& {a_1} = - 2{\text{ and }}{a_2} = - 1 \cr
& {\text{Find }}d \cr
& d = {a_{n + 1}} - {a_n} \cr
& d = {a_2} - {a_1} \cr
& d = - 1 - \left( { - 2} \right) \cr
& d = 1 \cr
& \cr
& {\text{The }}n{\text{th Term of an Arithmetic Sequence is given by}} \cr
& {a_n} = {a_1} + \left( {n - 1} \right)d \cr
& {\text{Then}} \cr
& {a_n} = - 2 + \left( {n - 1} \right)\left( 1 \right) \cr
& {a_n} = - 2 + n - 1 \cr
& {a_n} = n - 3 \cr
& {\text{The domain is }}D:\left\{ {1,2,3,4,5,6} \right\} \cr
& {\text{The range is }}R:\left\{ { - 2, - 1,0,1,2,3} \right\} \cr} $$
