Chapter 6, Problem 30CR

To determine

To write:An equation for the nth term of the geometric sequence. Then find $a_9$

Answer to Problem 30CR

An equation for nth term of the sequence is $a_n=5{(-2)}^{n-1}$

  $a_9=1280$

Explanation of Solution

Given information:The sequence $5,-10,20,-\mathrm{40...}$

Calculation:The first term is 5 and the common ratio is $-2$.

  $a_n=a_1{r}^{n-1}$

  $a_n=5{(-2)}^{n-1}$

Thus, an equation for nth term of the sequence is $a_n=5{(-2)}^{n-1}$

Using the equation to find the 9^th term,

  $\begin{array}{l}$ a_n=5{(-2)}^{n-1}$$ \Rightarrow a_9=5{(-2)}^{9-1}$$ \Rightarrow a_9=5{(-2)}^8$\Rightarrow a_9=5\times 256\\ \Rightarrow a_9=1280\end{array}$

Thus, 9^th term of the geometric sequence is $a_9=1280$