Question

What is the recursive formula for the sequence 3, -1, -5, -9, -13,...? a1 = 3, an = (an - 1)(-4) a1 = 3, an = (an - 1) – 4 a1 = 3, an = (an - 1)(4) a1 = 3, an = (an - 1) + 4

Answer 1

`a_(n)` =
`a_(n-1)` - 4,
`a_(1)` = 3

Explanation:

A recursive formula allows us to find the next term in the sequence from the previous term.

note the difference between the terms in the sequence

= - 13 - ( - 9) = - 9 - (- 5) = - 5 - (- 1) = - 1 - 3 = - 4

That is to obtain any term in the sequence we subtract 4 from the previous term, hence

`a_(n)` =
`a_(n-1)` - 4,
`a_(1)` = 3