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GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 25

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The closed form for the $n^{th}$ term of the sequence with generating function $\frac{1}{1-ax}$ is $a^n$

The closed form for the $n^{th}$ term of the sequence with generating function $\frac{x}{1-ax}$ is $a^{n-1}$

$\therefore \frac{9x}{1-2x}$ corresponds to $9.2^{n-1}$ and $\frac{x}{1-x}$ corresponds to $1.$

Adding them we get the answer as option D.
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