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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, . . .

See The Solution Submitted by Brian Smith    
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Solution Puzzle Solution Comment 6 of 6 |

The (2n-1)th and the (2n)th term of the given sequence S(p)(say) is given by:
S(2n-1) + i*S(2n) = (1+i)^n

Substituting n =7 in the above relationship , we have:

(1+i)^7 = 29 + 278*i
Or, S(13) + i*S(14) =  29 + 278*i

Since no real number can equal a complex number, this is possible iff:

S(13) = 29 and S(14) = 278

Consequently, the required next two numbers in the given  sequence are 29 and 278.

 

Edited on November 10, 2007, 4:41 am
  Posted by K Sengupta on 2007-11-10 04:40:36

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