What are the next numbers in this sequence?

4, 5, 8, 8, 9, 9, 12, 13, 13, 13, ?, ?

this is what i did in order to get my second answer 14, 17.

in the sequence

4, 5, 8, 8, 9, 9, 12, 13, 13, 13, ...

i subtracted each nth term to n.

ex. 4-1 = 3, 5-2 = 3, 8-3 =5 and so on..

and the result is

3, 3, 5, 4, 4, 3, 5, 5, 4, 3, ...

if you notice, there is a repetition of number and the only numbers are 3, 4, and 5.

what i observed also are:

* the middle of two 3's and two 4's is 5.

*the middle of two 4's and two 5's is 3.

therefore, the middle of two 5's and two 3's is 4 since it has only 3 digits 3, 4, 5.

if we continue the latter sequence, it will become

3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 3, 5, ...

the required answer is just to add the terms 3 and 5 to its nth term.

3 + 11 = 14        and

5 + 12 = 17.

Posted by nickson on 2005-08-06 10:19:09