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Sequence Sum (Posted on 2003-12-08) Difficulty: 2 of 5
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?

See The Solution Submitted by Gamer    
Rating: 2.6000 (5 votes)

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Solution Puzzle Solution: An Attempt to generalisation Comment 8 of 8 |

Let the first two terms be x and y.
Then, in conformity with the tenets inclusive of the problem under reference:

Third Term is y-x; Fourth term is -x; Fifth term is -y while the Sixth Term is x-y.

So, summing over every sixth term we would always obtain 0 as a result.

Accordingly, it can be said that in general:
(i) The sum of the first 6N terms is 0.
(ii) The sum of the (6P+1) th through 6Qth term is 0, whenever Q>P and both P and Q are positive integers.

It is thus a trivial matter to substitute N = 1000 in (i) and obtain zero as the required solution to the given problem. 

  Posted by K Sengupta on 2007-03-16 11:07:13
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