What Comes Ninth?

Date: 11/07/2010 at 12:17:21
From: MONA
Subject: Sequencing numbers

3, 9, 4, 5, 25, 20, 21, 441.

What is the next number?

Date: 11/07/2010 at 12:28:42
From: Doctor Ali
Subject: Re: Sequencing numbers

Hi Mona!

Thanks for writing to Dr. Math.

See below:

    3     -> raise to the second power ->   9
    9     -> subtract by 5 ->               4
    4     -> add 1 ->                       5

Then those three steps start again, beginning from the result of the third
operation:

    5     -> raise to the second power ->   25
    25    -> subtract by 5 ->               20
    20    -> add 1 ->                       21

And the pattern repeats:

    21    -> raise to the second power ->   441
    441   -> subtract by 5 ->               ...

Does that make sense?

Please write back if you still have any difficulties.

- Doctor Ali, The Math Forum
  http://mathforum.org/dr.math/