perplexus.info :: Sequences : Sequence Sum

Sequence Sum (Posted on 2003-12-08)

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?

Submitted by Gamer

Rating: 2.6000 (5 votes)

Solution: (Hide)

Express the first six terms in terms of the first two terms.
a
b
b-a
(b-a)-b or -a
-a-(b-a) or -b
-b-(-a) or -b+a

Every six terms have a sum of zero, so the first 1000 groups of zero add up to zero. (It doesn't matter what the first terms are.)

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Solution: An Attempt to generalisation	K Sengupta	2007-03-16 11:07:13
salution	hunter	2004-03-30 08:39:09
2 ways to solve	Bob Genisot	2003-12-09 12:35:22
Solution (No computer program used)	Penny	2003-12-08 11:31:45
re: In general	SilverKnight	2003-12-08 10:48:34
In general	Lee	2003-12-08 10:39:10
re: Solution	Popstar Dave	2003-12-08 10:36:05
Solution	Popstar Dave	2003-12-08 10:31:07

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