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Can You Find The Rule (Posted on 2003-05-02) Difficulty: 3 of 5
Find the rule below and name the next number in the sequence:

1,2,9,1000,???,

See The Solution Submitted by luvya    
Rating: 3.8571 (7 votes)

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Solution Puzzle Solution | Comment 10 of 11 |

Let T(i) be the ith term of the given sequence.
Then, it seems that in terms of the conditions inclusive of the given problem:
T(i) = (T(i-1) + 1)^(i-1)

Thus, T(0) = 1, T(2) = (1+1)^1, and so on:

Consequently, the required missing term 
The fifth term of the sequence
= T(5)
= (T(4) + 1))^4
= (1000 + 1)^4
=1004006004001

Edited on June 1, 2008, 12:41 am
  Posted by K Sengupta on 2007-03-05 11:34:05

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