Algebra 1 U.8 Write variable expressions for geometric sequences XPC 4)) Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence , where n=1 for the first term. -9.9,29.7,-89.1,ldots 4) Write your answer using decimals and integers. a_(n)=square (square )^n-1

The given sequence is -9.9, 29.7, -89.1, ...<br /><br />We can find the common ratio by dividing any term by its preceding term.<br />Common ratio (r) = $\frac{29.7}{-9.9} = -3$<br />Also, $\frac{-89.1}{29.7} = -3$<br /><br />The first term, $a_1 = -9.9$.<br /><br />The general formula for a geometric sequence is given by $a_n = a_1 \cdot r^{n-1}$, where $a_n$ is the nth term, $a_1$ is the first term, r is the common ratio, and n is the position of the term.<br /><br />In this case, $a_1 = -9.9$ and $r = -3$.<br />So, the equation for the sequence is:<br />$a_n = -9.9(-3)^{n-1}$<br /><br />Final Answer: The final answer is $\boxed{a_{n}=-9.9(-3)^{n-1}}$<br />