Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.3 Geometric Sequences; Geometric Series - 12.3 Assess Your Understanding - Page 824: 36

$a_n=4(\frac{1}{4})^{n-1}.$

We know that $a_n=a_1r^{n-1}.$ where $r$=common ration (we can get this by dividing any two consecutive terms) and $a_1$= the first term Here $a_1=4$ and $r=\frac{a_2}{a_1}=\frac{1}{4}$ Hence, here we have $a_n=4(\frac{1}{4})^{n-1}.$