Question

PLEASE HELP ME THIS IS DUE IN 10 MINUTES PLEASE HELP ME!! THANK YOU!!

Answer 1

The sequence is:

`\:\left\{a_(1,\:)a_2,\:a_3,\:a_4\right\}\:=\:\left\{-10,\:-23,\:-62,\:-179\right\}`

Explanation:

Given the recursive function

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

As the first term is -10.

i.e.

`a_1=-10`

Putting n = 2 to determine the 2nd term

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

`a_2=3a_(2-1)+7`

`a_2=3a_1+7`

`= 3(-10)+7` ∵
`a_1=-10`

`= -23`

Putting n = 3 to determine the 3rd term

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

`a_3=3a_(3-1)+7\:\:`

`a_3=3a_2+7\:\:\:\:\:`

`= 3(-23)+7` ∵
`a_2=-23`

`= -62`

Putting n = 4 to determine the 4th term

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

`a_4=3a_(4-1)+7`

`a_4=3a_3+7\:\:\:\:\:`

`= 3(-62)+7` ∵
`a_3=-62`

`=-179`

Therefore, the sequence is:

`\:\left\{a_(1,\:)a_2,\:a_3,\:a_4\right\}\:=\:\left\{-10,\:-23,\:-62,\:-179\right\}`