Algebra 2 (1st Edition)

$a_n=a_1\cdot(0.75)^{n-1}$
An infinite geometric series has a sum if and only if $|r|\lt1$, where $r$ is the common ratio. If it exists, then it equals $\frac{a_1}{1-r}$ where $a_1$ is the first term. $r=0.75$ because each triangle consists of $4$ smaller ones out of which $1$ is removed. Hence $a_n=a_1\cdot(0.75)^{n-1}$