Question

What are the first three terms of the sequence defined by the recursive function , and ?

Answer 1

The first three terms of the sequence are 6 , 10 , 8 ⇒ 2nd answer

Explanation:

* Lets study the rule at first:

-
`a_(n)=a_(n-1)-(a_(n-2)-4)`

∴
`a_(n)=a_(n-1)-a_(n-2)+4`

* That means to find a term add the difference between

the two consecutive term before it to 4.

* lets start with
`a_(6)=a_(5)-a_(4)+4`

∵
`a_(5)=-2,a_(6)=0`

∴
`0=-2 -a_(4)+4`

∴
`0=2-a_(4)`

∴
`a_(4)=2`

* Use
`a_(5)` to find
`a_(3)`

∵
`a_(5)=a_(4)-a_(3)+4`

∴
`-2=2-a_(3)+4`

∴
`-2=6-a_(3)`

∴
`a_(3)=6+2=8`

* Similar use
`a_(4)` to find
`a_(2)`

∵
`a_(4)=a_(3)-a_(2)+4`

∴
`2=8-a_(2)+4`

∴
`2=12-a_(2)`

∴
`a_(2)=10`

* Finally use
`a_(3)` to find
`a_(1)`

∵
`a_(3)=a_(2)-a_(1)+4`

∴
`8=10-a_(1) +4`

∴
`8=14-a_(1)`

∴
`a_(1)=14-8=6`

∴ The first three terms of the sequence are 6 , 10 , 8 ⇒ 2nd answer