Question

What is the recursive rule for this geometric sequence? 27,  9,  3,  1,  ... Enter your answers in the boxes.

Answer 1

Answer:

$a_n=a_{n-1}(\frac{1}{3})\\a_1=27$

Step-by-step explanation:

A recursive formula is a formula in which each term is based on the previous term.

In a geometric sequence, each term is found by multiplying the previous term by a constant.

To get from 27 to 9, then from 9 to 3, etc., we would multiply by 1/3.  This makes the common ratio 1/3.

The recursive formula for a geometric sequence is

$a_n=a_{n-1}(r)$, where $a_n$ represents the general term,  $a_{n-1}$, represents the previous term, and r represents the common ratio.

Plugging in our values, we have

$a_n=a_{n-1}(r)$

We also have to indicate what the first term, a₁, is.  In this sequence, it is 21.  This gives us

$a_n=a_{n-1}(\frac{1}{3})\\a_1=27$

Answer 2

Rule: Divide by three

The terms in this sequence can be determined by dividing the previous number by (positive) three. 

27/3 = 9

9/3 = 3

3/3 = 1... 

      and so on and so forth...

Hope this helps! :)