What are the next two numbers in the following sequence:
1, 2, -3, 4, -11, -2, -7, -24, 41, -38, 117, 44, . . .
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
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