Question

I need help with this question please help

Answer 1

6, 10, 8 is the correct answer.

Explanation:

Given that, the recursive function:

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

6th term,
`a_(6) =0`

5th term,
`a_(5) =-2`

To find:

First three terms of the sequence = ?

Solution:

Putting n = 6 in the recursive function:

`a_6=a_(5)-(a_(4)-4)\\\Rightarrow 0=-2-(a_(4)-4)\\\Rightarrow 2=-(a_(4)-4)\\\Rightarrow -2=(a_(4)-4)\\\Rightarrow -2+4=a_(4)\\\Rightarrow a_(4)=2`

Putting n = 5 in the recursive function:

`a_5=a_(4)-(a_(3)-4)\\\Rightarrow -2=2-(a_(3)-4)\\\Rightarrow -2-2=-(a_(3)-4)\\\Rightarrow 4=(a_(3)-4)\\\Rightarrow a_(3)=8`

Putting n = 4 in the recursive function:

`a_4=a_(3)-(a_(2)-4)\\\Rightarrow 2=8-(a_(2)-4)\\\Rightarrow 2-8=-(a_(2)-4)\\\Rightarrow 6=(a_(2)-4)\\\Rightarrow a_(2)=10`

Putting n = 3 in the recursive function:

`a_3=a_(2)-(a_(1)-4)\\\Rightarrow 8=10-(a_(1)-4)\\\Rightarrow 8-10=-(a_(1)-4)\\\Rightarrow -2=-(a_(1)-4)\\\Rightarrow 2=a_(1)-4\\\Rightarrow a_(1)=4+2\\\Rightarrow a_(1)=6`

So, first, second and third terms are 6, 10, 8.