Question:
We are studying number sequences at my school, Butler Middle School, Waukesha Wisconsin.

I CAN NOT figure out this sequence or how we continue this sequence...

3,2,6,5,15,14,___,___,___

Can you PLEASE help me ?

Thank You,
Justin Schessler

ps. my dad said this site might be a real help.

Hi Justin,

Sometimes these number or letter sequence problems are obvious like

sometimes they are bizarre like

and sometimes there is more than one set of rules that will generate the terms you have.
   For your problem

I don't see anything obvious and I don't recognize it as one of the more bizarre examples I have seen. The only pattern I see is:

• every even numbered term, (2, 5, 14) is one less than the previous term

• the first odd numbered term is 3 and after that each odd numbered term is 3 time the previous term.

• the seventh term is 3*(the sixth term) = 3*14 = 42

• the eighth term is one less than the seventh term, 42 - 1 = 41

• the ninth term is 3*(the eighth term) = 3*41 = 123

This may not be the sequence that is sought, but it consistently explains the first 6 terms.

Cheers,
Chris and Harley

By the way the letter sequence above in made from the first letters of the counting numbers, One, Two, Three, Four, ...