Answer:
The first three terms of the sequence are 6 , 10 , 8 ⇒ 2nd answer
Step-by-step explanation:
* Lets study the rule at first:
- [tex]a_{n}=a_{n-1}-(a_{n-2}-4)[/tex]
∴ [tex]a_{n}=a_{n-1}-a_{n-2}+4[/tex]
* That means to find a term add the difference between
the two consecutive term before it to 4.
* lets start with [tex]a_{6}=a_{5}-a_{4}+4[/tex]
∵ [tex]a_{5}=-2,a_{6}=0[/tex]
∴ [tex]0=-2 -a_{4}+4[/tex]
∴ [tex]0=2-a_{4}[/tex]
∴ [tex]a_{4}=2[/tex]
* Use [tex]a_{5}[/tex] to find [tex]a_{3}[/tex]
∵ [tex]a_{5}=a_{4}-a_{3}+4[/tex]
∴ [tex]-2=2-a_{3}+4[/tex]
∴ [tex]-2=6-a_{3}[/tex]
∴ [tex]a_{3}=6+2=8[/tex]
* Similar use [tex]a_{4}[/tex] to find [tex]a_{2}[/tex]
∵ [tex]a_{4}=a_{3}-a_{2}+4[/tex]
∴ [tex]2=8-a_{2}+4[/tex]
∴ [tex]2=12-a_{2}[/tex]
∴ [tex]a_{2}=10[/tex]
* Finally use [tex]a_{3}[/tex] to find [tex]a_{1}[/tex]
∵ [tex]a_{3}=a_{2}-a_{1}+4[/tex]
∴ [tex]8=10-a_{1} +4[/tex]
∴ [tex]8=14-a_{1}[/tex]
∴ [tex]a_{1}=14-8=6[/tex]
∴ The first three terms of the sequence are 6 , 10 , 8 ⇒ 2nd answer
