Answer:
The sequence is:
[tex]\:\left\{a_{1,\:}a_2,\:a_3,\:a_4\right\}\:=\:\left\{-10,\:-23,\:-62,\:-179\right\}[/tex]
Step-by-step explanation:
Given the recursive function
[tex]a_n=3a_{n-1}+7[/tex]
As the first term is -10.
i.e.
[tex]a_1=-10[/tex]
Putting n = 2 to determine the 2nd term
[tex]a_n=3a_{n-1}+7[/tex]
[tex]a_2=3a_{2-1}+7[/tex]
[tex]a_2=3a_1+7[/tex]
[tex]= 3(-10)+7[/tex] ∵ [tex]a_1=-10[/tex]
[tex]= -23[/tex]
Putting n = 3 to determine the 3rd term
[tex]a_n=3a_{n-1}+7[/tex]
[tex]a_3=3a_{3-1}+7\:\:[/tex]
[tex]a_3=3a_2+7\:\:\:\:\:[/tex]
[tex]= 3(-23)+7[/tex] ∵ [tex]a_2=-23[/tex]
[tex]= -62[/tex]
Putting n = 4 to determine the 4th term
[tex]a_n=3a_{n-1}+7[/tex]
[tex]a_4=3a_{4-1}+7[/tex]
[tex]a_4=3a_3+7\:\:\:\:\:[/tex]
[tex]= 3(-62)+7[/tex] ∵ [tex]a_3=-62[/tex]
[tex]=-179[/tex]
Therefore, the sequence is:
[tex]\:\left\{a_{1,\:}a_2,\:a_3,\:a_4\right\}\:=\:\left\{-10,\:-23,\:-62,\:-179\right\}[/tex]
