Question

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

Answer 1

Answer:

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

Step-by-step 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