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?

Of course it doesn't matter what the numbers are
The series cancels to give
a, b, (b-a),-a, -b, (-b+a), a, b, (b-a)........
The sum of the first 6 terms are 0 and from then it repeats - so the sum of the first n terms is 0 if n/6 is an integer.
Penny will be pleased to hear this theory is verified for the first 6 000 000 000 000 000 000 terms. I've just had my friend at NASA run through it at work and he informs me it does, indeed, sum to zero

Posted by Lee on 2003-12-08 10:39:10