Question

I need some help on my math, i have a image of it.

Answer 1

`a_(n)` = 4 - 3(n - 1) and a₈ = - 17

Explanation:

a recursive formula is of the form

`a_(n)` =
`a_(n-1)` + d ( d is the common difference )

compare to

`a_(n)` =
`a_(n-1)` - 3

then d = - 3

the explicit formula for an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term

here a₁ = 4 and d = - 3 , then

`a_(n)` = 4 - 3(n - 1) ← explicit formula

then

a₈ = 4 - 3(8 - 1) = 4 - 3(7) = 4 - 21 = - 17