1. **State the problem:** Given a generating function $G(x)$ of a sequence $(a_n)$, find the first ten terms $a_0, a_1, \dots, a_9$ of that sequence. 2. **Identify the generating function:** The problem does not specify the exact form of $G(x)$. Please provide the generating function explicitly, for example, $G(x)=\frac{1}{1-x}$ or any other function. 3. **Understand generating functions:** A generating function $G(x)=\sum_{n=0}^\infty a_n x^n$ encodes the sequence $(a_n)$ as coefficients of powers of $x$. 4. **Extract coefficients:** To find the sequence values $a_n$, expand $G(x)$ as a power series around $x=0$ and read off coefficients of $x^n$. 5. **Calculate first ten terms:** Once the generating function is provided, perform series expansion or algebraic manipulation to find $a_0, a_1, ..., a_9$. **Please provide the explicit form of the generating function to proceed with the detailed steps and final answer.**