Find the rule below and name the next number in the sequence:

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

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**