Answer
$$\eqalign{
& 1,3,4,7,11 \cr
& {\text{The sequence is neither geometric nor arithmetic}} \cr} $$
Work Step by Step
$$\eqalign{
& {a_1} = 1,\,\,\,{a_2} = 3 \cr
& {a_n} = {a_{n - 2}} + {a_{n - 1}},\,\,\,{\text{if }}n \geqslant 3 \cr
& \cr
& n = 3 \cr
& {a_3} = {a_{3 - 2}} + {a_{3 - 1}} \cr
& {a_3} = {a_1} + {a_2} \cr
& {a_3} = 1 + 3 \cr
& {a_3} = 4 \cr
& \cr
& n = 4 \cr
& {a_4} = {a_{4 - 2}} + {a_{4 - 1}} \cr
& {a_4} = {a_2} + {a_3} \cr
& {a_4} = 3 + 4 \cr
& {a_4} = 7 \cr
& \cr
& n = 5 \cr
& {a_5} = {a_{5 - 2}} + {a_{5 - 1}} \cr
& {a_5} = {a_3} + {a_4} \cr
& {a_5} = 4 + 7 \cr
& {a_3} = 11 \cr
& \cr
& 1,3,4,7,11 \cr
& {\text{The sequence is neither geometric nor arithmetic}} \cr} $$
