Question

What is the next fraction in this sequence? Simplify your answer. 5/6 ,5/9 ,10/27 ,20/81  

Answer 1

My first question is whether this is an arith. sequence or a geom. sequence.

Assuming that it's geom., let's find the multiplier of 5/6 that produces 5/9:

5/9
---- = 6/9 = 2/3
5/6

Next, check whether (2/3)(5/6) actually produces 5/9:  10/18 = 5/9  (yes).
The next step is to determine whether 2/3 times 5/9 produces 10/27:

2     5
-- * --- = 10/27   Yes.
3     9

So, it appears that you have a geometric sequence with first term 5/6 and common ratio 2/3.

To find the next term of the sequence, multiply the last given term  (20/81)by the common ratio (2/3); we get 20*2
                                            --------  =  ??
                                             3(81)