Q:

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

Accepted Solution

A:
Answer:The first three terms of the sequence are 6 , 10 , 8 β‡’ 2nd answerStep-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 Β  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 β‡’ 2nd answer