Question

How do you write the first five terms of the sequence `a_n=n(n^2-6)`?

Answer 1

`-5,-4, 9, 40, 95`

Explanation:

Just plug in `n=1,2,3,4,5` for the formula to get the first five terms.

We know that the `n`th term of the sequence is defined by

`a_n=n(n^2-6)`

So,

`a_1=1(1-6)=-5` (first term)

`a_2=2*(4-6)=-4` (second term)

`a_3=3(9-6)=9` (third term)

`a_4=4(16-6)=40` (fourth term)

`a_5=5(25-6)=95` (fifth term)

Hence, the first five terms of the sequence `a_n=n(n^2-6)` are

`-5,-4, 9, 40, 95`

Answer 2

`-5,-4,9,40,95`

Explanation:

`"substitute corresponding value for n into "a_n=n(n^2-6)`

`a_n=n(n^2-6)=n^3-6n`

`rArra_(color(red)(1))=(color(red)(1))^3-(6xxcolor(red)(1))=1-6=-5`

`rArra_(color(red)(2))=(color(red)(2))^3-(6xxcolor(red)(2))=8-12=-4`

`rArra_(color(red)(3))=(color(red)(3))^3-(6xxcolor(red)(3))=27-18=9`

`rArra_(color(red)(4))=(color(red)(4))^3-(6xxcolor(red)(4))=64-24=40`

`rArra_(color(red)(5))=(color(red)(5))^3-(6xxcolor(red)(5))=125-30=95`