Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.3 Geometric Sequences; Geometric Series - 12.3 Assess Your Understanding - Page 824: 31

$0.00000004.$

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 $a_1=0.4$ and $r=\frac{a_2}{a_1}=\dfrac{0.04}{0.4}=0.1$ Hence, here we have $a_n=0.4(0.1)^{n-1}.$ Therefore $a_{8}=0.4(0.4)^{8-1}\\=0.00000004.$