Subject: Number Sequences
Name: Justin Schessler
Who is asking: Student
Level: Middle

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...


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

2, 4, 8, 16, 32, __, __, ...

sometimes they are bizarre like

O, T, T, F, F, S, S, __, __, ...

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

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

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 terms you have satisfy these rules and continuing gives
  • 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.

Chris and Harley

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


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