Chapter 9.8, Problem 49SR

To determine

To evaluate: the value of $a{\left(1+r\right)}^t$ to the nearest hundredth for given values.

Answer to Problem 49SR

The 5^th, 6^th, 7^th terms are −0.03125, −0.015625, and −0.0078125.

Explanation of Solution

Given:

  $-5,-10,-20,-40,\mathrm{......}$

Evaluating,

5^th term,

  $\begin{array}{c}a{r}^5=1{\left(-\frac{1}{2}\right)}^5\\ =-0.03125\end{array}$

6^th term,

  $\begin{array}{c}a{r}^6=1{\left(-\frac{1}{2}\right)}^6\\ =-0.015625\end{array}$

7^th term,

  $\begin{array}{c}a{r}^7=1{\left(-\frac{1}{2}\right)}^7\\ =-0.0078125\end{array}$

So,

The 5^th, 6^th, 7^th terms are −0.03125, −0.015625, and −0.0078125.