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Next Numbers Please #5 (Posted on 2004-12-05) Difficulty: 3 of 5
What are the next two numbers in the following sequence:

1, 2, -3, 4, -11, -2, -7, -24, 41, -38, 117, 44, . . .

  Submitted by Brian Smith    
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Solution: (Hide)
Take the values in pairs as complex numbers:
1+2i, -3+4i, -11-2i, -7-24i, 41-38i, 117+44i

As a sequence of complex numbers, it is a series of powers of 1+2i:
(1+2i)^1 = 1+2i
(1+2i)^2 = -3+4i
(1+2i)^3 = -11-2i
(1+2i)^4 = -7-24i
(1+2i)^5 = 41-38i
(1+2i)^6 = 117+44i

The next power is (1+2i)^7 = 29+278i, so the next two terms are 29 and 278

Sequence:1, 2, -3, 4, -11, -2, -7, -24, 41, -38, 117, 44, 29, 278.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle SolutionK Sengupta2007-11-10 04:40:36
20th??sragen2004-12-23 01:08:01
re: great...Spork2004-12-09 21:05:25
great...sragen2004-12-08 02:30:15
solution and explanationJoe Ruby2004-12-05 23:02:13
answer????wof2004-12-05 18:37:48
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