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Enter the first 4 terms of the sequence defined by the given rule. Assume that the domain of each function is the set of whole numbers greater than 0.

f(1) = 390,625, f (n) = f (n − 1)

The first 4 terms of the sequence are ____, ____, ____, and ____.

Respuesta :

MrRoyal

Answer:

The first four terms is: 390625, 625, 25, 5

Step-by-step explanation:

Given

[tex]f(n) = \sqrt{f(n-1)}[/tex]

To determine the first 4 terms.

We have

[tex]f(1) = 390625[/tex]

[tex]f(2) = \sqrt{f(2 - 1)}[/tex]

[tex]f(2) = \sqrt{f(1)}[/tex]

Substitute 390625 for f(1)

[tex]f(2) = \sqrt{390625}[/tex]

[tex]f(2) = 625[/tex]

For f(3), we have

[tex]f(3) = \sqrt{f(3-1)}[/tex]

[tex]f(3) = \sqrt{f(2)[/tex]

[tex]f(3) = \sqrt{625[/tex]

[tex]f(3) = 25[/tex]

For f(4), we have

[tex]f(4) = \sqrt{f(4-1)[/tex]

[tex]f(4) = \sqrt{f(3)[/tex]

[tex]f(4) = \sqrt{25[/tex]

[tex]f(4) = 5[/tex]

Hence, the first four terms is:

390625, 625, 25, 5

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