How do I find the nth term?

Question

I should know how to do this but it is late at night and I cannot for the life of me figure it out. 

I am trying to figure out the nth term of the sequence 2,6,18,54,162... I realize it's just being multiplied by three but I don't know how to write out a rule for that.

Answer 1

You are correct about being multiplied by 3.  A particular term divided by the previous term is 3:

 

6/2 = 3

18/6 = 3

54/18 = 3

162/54 = 3

 

So the next term N must satisfy

 

N/162 = 3

 

N = 3(162) = 486