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caylus
Hello,

[tex] x_{1} =65536\\ x_{n+1} =\sqrt{ x_{n}}\\\\ x_{1}=65536\\ x_{2} =\sqrt{65536}=256\\ x_{3} =\sqrt{256}=16\\ x_{4} =\sqrt{16}=4\\ x_{5} =\sqrt{4}=2\\ x_{6} =\sqrt{2}\\ ...[/tex]
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The next number after 65536, 256, 16, is 4, 2.

What is a number sequence?

  • A number sequence is a list of numbers that are connected by a rule.
  • If you work out the rule, you can work out the next numbers in the sequence.
  • An Arithmetic Sequence is made by adding the same value of a number each time with the last number.
  • A Geometric Sequence is made by multiplying by the same value of number each time with the last number.

[tex]$x_{1}=65536$x_{n+1}=\sqrt{x_{n}}\\$x_{1}=65536\\$x_{2}=\sqrt{65536}=256\\$x_{3}=\sqrt{256}=16\\$x_{4}=\sqrt{16}=4\\$x_{5}=\sqrt{4}=2\\$x_{6}=\sqrt{2}$[/tex]

No infinite sequence is determined purely by its first few terms.

To learn more about the number sequence refer to:

https://brainly.com/question/12246947

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