What is the difference of the geometric sequence?

Question

_____,____,1,-3,9

 

Answer 1

Geometric sequences have a common ratio r (arithmetic sequences have a common difference d).  You can figure out the common ratio by dividing 2 successive terms in the geometric sequence  

 

r = (-3) / 1 = -3  

 

Note that r is also equal to  9/(-3) = -3.  If these 2 values were not the same ratio then this would not be a geometric sequence.  

 

Once you know what r is you can figure out the missing terms in the sequence.  Since each term is r times the term that precedes it, it follows that each preceding term is (1/r) times the term that follows it.  

 

So the second term is (1/(-3)) * 1 = -1/3  

and the first term is (1/(-3)) * (-1/3) = 1/9  

 

So the five terms of the sequence are  1/9, -1/3, 1, -3, 9  

 

You should check each pair of successive terms to make sure the common ratio is the same.