Question

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 ____.

Answer 1

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

Explanation:

Given

`f(n) = √(f(n-1))`

To determine the first 4 terms.

We have

`f(1) = 390625`

`f(2) = √(f(2 - 1))`

`f(2) = √(f(1))`

Substitute 390625 for f(1)

`f(2) = √(390625)`

`f(2) = 625`

For f(3), we have

`f(3) = √(f(3-1))`

`f(3) = \sqrt{f(2)`

`f(3) = \sqrt{625`

`f(3) = 25`

For f(4), we have

`f(4) = \sqrt{f(4-1)`

`f(4) = \sqrt{f(3)`

`f(4) = \sqrt{25`

`f(4) = 5`

Hence, the first four terms is:

390625, 625, 25, 5