Chapter 8.5, Problem 55E

To determine

To give:an example of a real-life situation that represent a recursive rule which does not approach a limit.

Answer to Problem 55E

  $a_n=\left(1+\frac{0.725}{100}\right)a_{n-1}-950$ .

Explanation of Solution

Given:

Represent a real-life situation.

Calculation:

An example of a real-life situation modeled with a recursive sequence might be the balance for paying the mortgage with an annual interest rate compounded monthly.

Let us consider:

  $\begin{array}{l}\text{Mortgage value}=\$100,000\\ \text{Rate of interest}=7.25\%\\ \text{Monthly payment}=\$950\end{array}$

Now, recursive sequence is

  $\begin{array}{l}{a}_1=100,000\\ a_n=\left(1+\frac{0.725}{100}\right)a_{n-1}-950\end{array}$

Thus, the recursive rule does not approach a limit.