Question

Please help answer this question as soon as possible!

Answer 1

`a_(n)` = 10.5 - 3n

Explanation:

The explicit rule for an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

A recursive formula has the form

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

Given

`a_(n)` =
`a_(n-1)` - 3 ⇒ d = - 3

Thus explicit rule with a₁ = 7.5 and d = - 3

`a_(n)` = 7.5 - 3(n - 1) = 7.5 - 3n + 3 = 10.5 - 3n