Suppose G is the generating function for the sequence 4, 7, 10, 13, 16, 19,…, the find a generating function (in terms of G) for the sequence of differences between terms.(a) (1−x)G−4/x(b) (1−x)G−4/x^3(c) (1−x)G+6/x(d) (1−x)G−x^2This question was addressed to me in a job interview.Origin of the question is Discrete Probability topic in section Discrete Probability of Discrete Mathematics

Suppose G is the generating function for the sequence 4, 7, 10, 13, 16

1.	Suppose G is the generating function for the sequence 4, 7, 10, 13, 16, 19,…, the find a generating function (in terms of G) for the sequence of differences between terms.(a) (1−x)G−4/x(b) (1−x)G−4/x^3(c) (1−x)G+6/x(d) (1−x)G−x^2This question was addressed to me in a job interview.Origin of the question is Discrete Probability topic in section Discrete Probability of Discrete Mathematics
Answer» The correct ANSWER is (a) (1−x)G−4/x The explanation: (1−x)G = 4 + 3X + 6x^2 + 9x^3 +⋯ which can be accepted. We can COMPUTE it like this: 3 + 6x + 9x^2 + ⋯ = (1−x)G−4/x.

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