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Enter a recursive rule for the geometric sequence.

2, 6, 18, 54, …

a1=____  ;  an=____

The one and the n are both subscript facing down so like an exponent just a lower exponent.

 Dec 20, 2018
 #1
avatar+17163 
+2

a1=2       an = a(n+1)/3    (I think)      or maybe    a(n-1) = a(n) / 3    

 Dec 20, 2018
 #2
avatar+98005 
+2

a1  = 2  =  1st term

 

We need to find the common ratio from one term to the next

 

r =  common ratio   =    subsequent term / previous term  = 6/2 = 3

 

To find any term, an.....we have

 

an =  a1 * r(n - 1)  =    2(3)rn-1      where n is the nth term

 

So....for example....if we wanted the 4th term...we have

 

2 (3) 4-1  =  2(3)3  =    2*27    =   54      .....as expected  !!!

 

 

cool cool cool

 Dec 20, 2018
 #3
avatar+17163 
+1

Thanx for the clarification, Chris !   

ElectricPavlov  Dec 20, 2018

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