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lubasha [3.4K]
3 years ago
13

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

Mathematics
2 answers:
ANEK [815]3 years ago
8 0

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

8_murik_8 [283]3 years ago
4 0
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! :)
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