11  22  33  44  a  
37  61  85  109  b  
33  66  132  264  c  
3  9  27  81  d  
10  9  60  90  e 
Hint: Scroll down this page to see the extension activity (Extension 2) for help with the fifth sequence above.
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Can you also find a general rule for predicting the nth term of the sequences?
n^{th} term
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Teacher, do your students have
access to computers? 

Here a concise URL for a version of this page without the comments.
Here is the URL which will take them to sequences of patterns made with matchsticks.
There is an old tradition of using logic puzzles to test job candidates at interview. Here is the version of part (e) above that is said to be asked of Google job candidates:
Count the number of letters in the words of the numbers in the sequence.
The numbers are the largest numbers that can be spelled in a given number of letters.
Some say 96 but others have said 'one googol' or even 'ten googol'! More information about this question can be found in the excellent book 'Are you smart enough to work at Google?' by William Poundstone."