Answer:
1, 2, 8, 128, 32768
Step-by-step explanation:
[tex]recursive \: formula: \\ a _{n} = 2. {( a_{n - 1} )}^{2} \\ \\ a _{1} = 1...(given) \\ \\ a _{2} = 2. {( a_{2 - 1} )}^{2} = 2 {(a _{1} )}^{2} = 2 {(1)}^{2} \\ \\ a _{2} = 2\\ \\a _{3} = 2. {( a_{3 - 1} )}^{2} = 2 {(a _{2} )}^{2} = 2 {(2)}^{2} \\ \\ a _{3} = 8\\ \\a _{4} = 2. {( a_{4 - 1} )}^{2} = 2 {(a _{3} )}^{2} = 2 {(8)}^{2} \\ \\ a _{4} = 128\\ \\a _{5} = 2. {( a_{5 - 1} )}^{2} = 2 {(a _{4} )}^{2} = 2 {(128)}^{2} \\ \\ a _{5} = 32,768\\ \\[/tex]
Thus the first five terms are: 1, 2, 8, 128, 32768.
