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(n)=n3-7

The first 4 terms of the sequence are______,______,______,_______.​

Answer 1

Given:

The given rule is

`f(n)=n^3-7`

Domain of the function is the set of whole numbers greater than 0.

To find:

The first 4 terms of the sequence.

Solution:

We have,

`f(n)=n^3-7`

Domain of the function is the set of whole numbers greater than 0. So, the domain for first four terms of the sequence are 1, 2, 3 and 4 respectively.

For n=1,

`f(1)=(1)^3-7`

`f(1)=1-7`

`f(1)=-6`

For n=2,

`f(2)=(2)^3-7`

`f(2)=8-7`

`f(2)=1`

For n=3,

`f(3)=(3)^3-7`

`f(3)=27-7`

`f(3)=20`

For n=4,

`f(4)=(4)^3-7`

`f(4)=64-7`

`f(4)=57`

Therefore, the first 4 terms of the sequence are -6, 1, 20, 57 respectively.