which recursive sequence would produce the sequence 9,-49,241

Answer 1

y = (-5(a_n-1) - 4).

In this example you can notice that the |a| increases with each new term, so you can assume that the previous number is getting multiplied by some factor. You also notice that the sign changes, so it must be a negative factor being multiplied. To do this, simply divide the term by the previous term (-49/9) = -5.444. This is closer to 5 than 6, so use -5 as your factor, then you just have to determine how to account for the extra difference to get the - 4 part of the equation. (-5 x 9 = -45, -45 - 4 = -49)