## Thinking Mathematically (6th Edition)

$16,\,\,8\text{,}\,\,\text{4},\,\,2,\,\,1\text{ and }\frac{1}{2}$
For the second term $n=2$: \begin{align} & {{a}_{2}}=a{{r}^{n-1}} \\ & =16{{\left( \frac{1}{2} \right)}^{2-1}} \\ & =16{{\left( \frac{1}{2} \right)}^{1}} \\ & =8 \end{align} For the third term$n=3$: \begin{align} & {{a}_{3}}=a{{r}^{3-1}} \\ & =16{{\left( \frac{1}{2} \right)}^{2}} \\ & =16\times \frac{1}{4} \\ & =4 \end{align} For the fourth term$n=4$: \begin{align} & {{a}_{4}}=a{{r}^{4-1}} \\ & =16{{\left( \frac{1}{2} \right)}^{3}} \\ & =16\times \frac{1}{8} \\ & =2 \end{align} For the fifth term$n=5$: \begin{align} & {{a}_{5}}=a{{r}^{5-1}} \\ & =16{{\left( \frac{1}{2} \right)}^{4}} \\ & =16\times \frac{1}{16} \\ & =1 \end{align} For the sixth term$n=6$: \begin{align} & {{a}_{6}}=a{{r}^{6-1}} \\ & =16{{\left( \frac{1}{2} \right)}^{5}} \\ & =16\times \frac{1}{32} \\ & =\frac{1}{2} \end{align} Hence, the first six terms of the geometric sequence are$16,\,\,8\text{,}\,\,\text{4},\,\,2,\,\,1\text{ and }\frac{1}{2}$.