In a certain sequence, the next term is found by taking the number before it minus the number two numbers before it.

For example, in the sequence a, b, c, d... c = b-a, d = c-b, and so on.

Starting with 54 and 93, what would be the sum of the first six thousand terms?

With 54 as the first number and 93 as the second; this will give us 39 as the third, then -54, -93 and -39. These six numbers will continuously cycle. Therefore taking the sum of the first 6n terms (where n is any positive integer) will give a sum of 0. As 6000 = 6*1000 and 1000 is certainly a positive integer, the answer in this case is 0.

Posted by Popstar Dave on 2003-12-08 10:31:07