Chapter 6.6, Problem 26E

To determine

To find:An equation for the nth term of the geometric sequence. Then find $a_6$ .

Answer to Problem 26E

The nth term of the geometric sequence is $a_n=0.6\cdot {(-5)}^{n-1}$ and $a_6=-1875$ .

Explanation of Solution

Giveninformation:

The sequence is $0.6,-3,15,-75,\mathrm{...}$

Formula used:

The nth term of a geometric sequence is given by $a_n=a_1{r}^{n-1}$ , where $a_1$ represents the first term of the sequence and $r$ represents the common ratio.

From the given sequence we can notice that $a_1=0.6$ and $r=-5$ .

Therefore, the nth term of the sequence is

  $\begin{array}{l}{a}_n=a_1{r}^{n-1}\\ $ \Rightarrow a_n=0.6\cdot {(-5)}^{n-1}$\end{array}$

To find $a_6$ , substitute 6 for $n$ .

  $a_6=0.6\cdot {(-5)}^{6-1}=0.6\cdot {(-5)}^5=-1875$

Conclusion:

Therefore, the nth term of the geometric sequence is $a_n=0.6\cdot {(-5)}^{n-1}$ and $a_6=-1875$ .