Question

PLEASE HELP ME WITH THIS ALGEBRA QUESTION!! THANK YOU!!

Answer 1

The first four terms of the sequence are: {-10,-23,-62,-179}

Explanation:

Given recursive formula is:

`a_n = 3a_(n-1)+7`

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

`a_2 = 3a_(2-1)+7\\a_2 = 3a_1+7\\a_2 = 3(-10)+7\\a_2 = -30+7\\a_2 = -23`

Putting n=3

`a_3 = 3a_(3-1)+7\\a_3 = 3a_2+7\\a_3 = 3(-23)+7\\a_3 = -69+7\\a_3 = -62`

Putting n=4

`a_4 = 3a_(4-1)+7\\a_4 = 3a_3+7\\a_4 = 3(-62)+7\\a_4 = -186+7\\a_4 = -179`

Hence,

The first four terms of the sequence are: {-10,-23,-62,-179}