Chapter 6.5, Problem 36E

To determine

To describe: Describe and correct the error in writing the next three terms of the geometric sequence.

Answer to Problem 36E

The values of common ratio and the expression for general term are incorrect. The correct values are $r=6$ and $a_n=-2{(6)}^{n-1}$ .

Explanation of Solution

Giveninformation:

  

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 $a_1=-2$ and $r=6$ .

But it is given that $r=-6$ which is incorrect so the general term given is also incorrect.

Conclusion:

Therefore, the nth term of the given sequence would be

  $\begin{array}{l}{a}_n=a_1{r}^{n-1}\\ $ \Rightarrow a_n=-2\cdot {(6)}^{n-1}$\end{array}$