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