Question

How do I write a recursive formula for this sequence? 2, 6, 18, 54, 162, ... I already know the common difference is x3.

Answer 1

For the sequence 2, 6, 18, 54, ..., the explicit formula is: an = a1 ! rn"1 = 2 ! 3n"1 , and the recursive formula is: a1 = 2, an+1 = an ! 3 . In each case, successively replacing n by 1, 2, 3, ... will yield the terms of the sequence. See the examples below.