## Thinking Mathematically (6th Edition)

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