Find the rule behind this number sequence, and list the next three numbers:

..., 2, 23/3, 15, 121/5, 106/3, ..., ..., ...

(Hint: the first number listed is the second term of the sequence)

The numbers are right. Here's the rule:

Put each number as a fraction with the denominators increasing by 1 for each fraction, starting with 2. (4/2, 23/3, 60/4, etc.)

Then take the numerators of the resulting fraction. Subtracting a numerator from the numerator that follows it yields a number. There is a number for each pair of numerators. Subtracting one of those numbers from the one that follows it gives a multiple of 6. The first of these 18.

Ex:

23-4=19
60-23=37
37-19=18

60-23=37
121-60=61
61-37=24

121-60=61
212-121=91
91-61=30

As you can see, the differences of the third equation for each set are consecutive multiples of 6.

Posted by Joe on 2005-11-08 19:00:21