• Jan 15th 2007, 02:45 PM
WzMath16
Hey everyone, I need to find patterns and continue each sequence to the next two numbers in the sequence. I was able to solve most of them but here are the 5 I'm completely stuck on... I'd appreciate any help. Thanks :)

1,4,9,16,27,_,_
1,1,1,3,5,9,17,_,_
0,5,8,8,2,3,5,2,9,4,_,_
10,40,90,61,52,63,94,_,_
2,7,1,8,2,8,1,8,2,8,4,5,_,_

Thanks again for any help :)
• Jan 15th 2007, 03:12 PM
Plato
Here a most useful site for these problems:
The On-Line Encyclopedia of Integer Sequences
• Jan 15th 2007, 04:39 PM
Soroban
Hello, WzMath16!

I got a few of them . . .

Quote:

\$\displaystyle 2)\;\;1,\,1,\,1,\,3,\,5,\,9,\,17,\,\hdots\$
The sequence begins with 1, 1, 1.

Each subsequent term is the sum of the preceding three numbers.

The next two terms are: .\$\displaystyle 5+9+17 \:=\:31\$ and \$\displaystyle 9 + 17 + 31 \:=\:57\$

Quote:

\$\displaystyle 4)\;\;10,\,40,\,90,\,61,\,52,\,63,\,94,\,\hdots\$
Reverse the numbers: .\$\displaystyle 01,\:04,\:09,\;16,\;25,\;36,\;49,\;\hdots\$

Got it?

Quote:

\$\displaystyle 5)\;\;2,\,7,\,1,\,8,\,2,\,8,\,1,\,8,\,2,\,8,\,4,\, 5,\,\hdots\$
These are the digits of the number \$\displaystyle e\:=\:2.718281828459045\hdots\$

• Jan 15th 2007, 07:06 PM
WzMath16
great, got them all. big thanks to the two of you for the help :)