How do you write the expression for the nth term of the sequence given #1/3, 2/9, 4/27, 8/81,...#?

1 Answer
Apr 9, 2017

#a_n=2^(n-1)/3^n#

Explanation:

First look at the bottom and see how it is increasing. #3, 9, 21, 81#. Looks like for each number it increases, it is #3# to the something power, so we have #3^n#. Now we will look at the top and try and guess what causes #1, 2, 4, 8#. Look's like it is #2# to the something power, except for #1#, so it must going to the #0# power, in order for it to turn #0#. Now we have #2^(n-1)#

This is why we have: #a_n=2^(n-1)/3^n#