Question

Write the first 4 terms of the sequence defined by the given rule.

Answer 1

Answer:

The first terms of this sequence should be:

f(1) = 65536

f(2) = 256

f(3) = 16

f(4) = 4

f(5) = 2

Explanation:

It is required to show the first tems of the sequence defined by the rule:

$f(n) = \sqrt{f(n-1)}$

In this sense, it is required to calculate f(n-1) in order to calculate f(n).

First term f(1) = 65536 is given in the problem. So, we can calcualte the other terms by replacing in the recursive formulation for this sequence as follows:

$f(1) =65536\\f(2) = \sqrt{f(1)}=\sqrt{65536} = 256\\f(2) = 256\\f(3) = \sqrt{f(2)}=\sqrt{256} =16\\f(3) = 16\\f(4) = \sqrt{f(3)}=\sqrt{16} =4\\f(4) = 4$

So we have that f(4) = 4.

Finally the term 5. f(5)

$f(5)=\sqrt{f(4)}=\sqrt{4} \\f(5) = 2$

Finally, we can conclude that The first terms of this sequence should be:

f(1) = 65536

f(2) = 256

f(3) = 16

f(4) = 4

f(5) = 2