Answer
$${a_n} = 3n - 7$$
Work Step by Step
$$\eqalign{
& {\text{From the figure we can see that }}{a_1} = - 4,\,\,\,\,{a_2} = - 1 \cr
& {\text{Find }}d \cr
& d = {a_{n + 1}} - {a_n} \cr
& d = {a_2} - {a_1} \cr
& d = \left( { - 1} \right) - \left( { - 4} \right) \cr
& d = 3 \cr
& \cr
& {\text{The }}n{\text{th Term of an Arithmetic Sequence is given by}} \cr
& {a_n} = {a_1} + \left( {n - 1} \right)d \cr
& {\text{Then}} \cr
& {a_n} = - 4 + \left( {n - 1} \right)\left( 3 \right) \cr
& {a_n} = - 4 + 3n - 3 \cr
& {a_n} = 3n - 7 \cr} $$
