Answer
$$\eqalign{
& 5,2, - 1, - 4, - 7 \cr
& {\text{The sequence is arithmetic}} \cr} $$
Work Step by Step
$$\eqalign{
& {a_1} = 5 \cr
& {a_n} = {a_{n - 1}} - 3,\,\,\,{\text{if }}n \geqslant 2 \cr
& {a_2} = {a_{2 - 1}} - 3 \cr
& {a_2} = {a_1} - 3 \cr
& {a_2} = 5 - 3 \cr
& {a_2} = 2 \cr
& \cr
& n = 3 \cr
& {a_3} = {a_{3 - 1}} - 3 \cr
& {a_3} = {a_2} - 3 \cr
& {a_3} = 2 - 3 \cr
& {a_3} = - 1 \cr
& \cr
& n = 4 \cr
& {a_4} = {a_{4 - 1}} - 3 \cr
& {a_4} = {a_3} - 3 \cr
& {a_4} = - 1 - 3 \cr
& {a_4} = - 4 \cr
& \cr
& n = 5 \cr
& {a_5} = {a_{5 - 1}} - 3 \cr
& {a_5} = {a_4} - 3 \cr
& {a_5} = - 4 - 3 \cr
& {a_5} = - 7 \cr
& \cr
& 5,2, - 1, - 4, - 7 \cr
& {\text{The sequence is arithmetic}} \cr} $$
