Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.3 Geometric Sequences; Geometric Series - 11.3 Assess Your Understanding - Page 844: 31

$0.00000004$

Work Step by Step

The $n^{th}$ term of a geometric sequence is given by the formula: $a_n=a_1r^{n-1}$ where $r$=common ratio and $a_1$= the first term The common ratio of a geometric sequence is equal to the quotient (ratio) of any term and the term before it: $\ r = \dfrac{a_n}{a_{n-1}}$ or, $r=\dfrac{a_2}{a_1}$ Here $a_1=0.4$ and and $a_2=0.04$, so $r=\dfrac{0.04}{0.4}=0.1$ So, $a_n=(0.4)(0.1)^{n-1}$ Therefore, $a_{8}=(0.4)(0.1)^{8-1} \approx 0.00000004$

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