Answer:
The first four terms of the sequence are: {-10,-23,-62,-179}
Step-by-step explanation:
Given recursive formula is:
[tex]a_n = 3a_{n-1}+7[/tex]
First term = a1 = -10
The first term is already known. In order to find the next terms, we will put n=2,3,4 in the recursive formula.
Putting n=2
[tex]a_2 = 3a_{2-1}+7\\a_2 = 3a_1+7\\a_2 = 3(-10)+7\\a_2 = -30+7\\a_2 = -23[/tex]
Putting n=3
[tex]a_3 = 3a_{3-1}+7\\a_3 = 3a_2+7\\a_3 = 3(-23)+7\\a_3 = -69+7\\a_3 = -62[/tex]
Putting n=4
[tex]a_4 = 3a_{4-1}+7\\a_4 = 3a_3+7\\a_4 = 3(-62)+7\\a_4 = -186+7\\a_4 = -179[/tex]
Hence,
The first four terms of the sequence are: {-10,-23,-62,-179}
