Sequences

I think your question is quite misleading.

It should be:
1 square needs 4 wire
4 squares need 12 wire (not 2 squares)
9 squares need 24 wire (not 3 squares)
16 need 40 (not 4)

Isn't it?

Then,
1st term:4 = 4 x 1
2nd term: 12 = 4 + 8 = 4 (1 + 2)
3rd term: 24 = 4 + 8 + 12 = 4 (1 + 2 + 3)
4nd term: 40 = 4 + 8 + 12 + 16 = 4(1 + 2 + 3 + 4)

So the nth term is 4 x (n - 1)th triangular number,
General term = 4n(n - 1)/2 = 2n(n - 1)

2007-07-30 09:24:10 補充：
Sorry, what I said is wrong, it should be:So the nth term is 4 x nth triangular number,General term = 4n(n 1)/2 = 2n(n 1)

Sn = 2n(n+1)
數左橫行先，有n+1行，每行用n條wire，
再數打直，一樣有n+1行，每行用n條wire，
所以 Sn = n(n+1) + n(n+1) = 2n(n+1)