The first term of a sequence is 9 . Each term after the first is 4

Choice D is correct. Since $w$ represents the $n$th term of the sequence and $9$ is the first term of the sequence, the value of $w$ is $9$ when the value of $n$ is $1$. Since each term after the first is $4$ times the preceding term, the value of $w$ is $9\left(4\right)$ when the value of $n$ is $2$. Therefore, the value of $w$ is $9\left(4\right)\left(4\right)$, or $9{\left(4\right)}^2$, when the value of $n$ is $3$. More generally, the value of $w$ is $9\left(4^{n-1}\right)$ for a given value of $n$. Therefore, the equation $w=9\left(4^{n-1}\right)$ gives $w$ in terms of $n$.

Choice A is incorrect. This equation describes a sequence for which the first term is $36$, rather than $9$, and each term after the first is $9$, rather than $4$, times the preceding term. 

Choice B is incorrect. This equation describes a sequence for which the first term is $4$, rather than $9$, and each term after the first is $9$, rather than $4$, times the preceding term.

Choice C is incorrect. This equation describes a sequence for which the first term is $36$, rather than $9$.