Respuesta :
Given:
The given rule is
[tex]f(n)=n^3-7[/tex]
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,
[tex]f(n)=n^3-7[/tex]
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,
[tex]f(1)=(1)^3-7[/tex]
[tex]f(1)=1-7[/tex]
[tex]f(1)=-6[/tex]
For n=2,
[tex]f(2)=(2)^3-7[/tex]
[tex]f(2)=8-7[/tex]
[tex]f(2)=1[/tex]
For n=3,
[tex]f(3)=(3)^3-7[/tex]
[tex]f(3)=27-7[/tex]
[tex]f(3)=20[/tex]
For n=4,
[tex]f(4)=(4)^3-7[/tex]
[tex]f(4)=64-7[/tex]
[tex]f(4)=57[/tex]
Therefore, the first 4 terms of the sequence are -6, 1, 20, 57 respectively.
