How to write the recursive rule for the sequence below?

Question

d-3e,2d-4e,3d-5e,4d-6e,...

Answer 1

First, we find the common difference or common ratio.

 

(2d - 4e) - (d - 3e) = d - e

 

(3d - 5e) - (2d - 4e) = d - e

 

 

We have a common difference, then the recursive formula is

 

f(x) = f(x - 1) + d - e

 

where      f(x - 1) = present term

               f(x) = next term