write a recursive formula for the sequence 6,9,13.5,20.25

Answer 1

Correcting the previous post, the common ratio is

r = 9 / 6 = 13.5 / 9 = 20.25 / 13.5

= 3/2

Hence, it IS a geometric series, and the recursive formula is as the previous post states.

Answer 2

First, note that this is NOT an Arithmetic Sequence (Common Difference) and it is NOT a Geometric Sequence (common ratio)..

For a recursive formula, there is often an obvious pattern between terms in the Sequence, so what is it?

term difference from previous term

6

9 3

13.5 4.5

20.25 6.75

So,

a₁ = 5

a_n = 1.5a_n-1 for n>1