Chapter 8.5, Problem 52E

To determine

To find:the 873rdterm of the sequence whose first term and nth term is given.

Answer to Problem 52E

A. $a_{873}=58.65$ .

Explanation of Solution

Given:

The nth term of given sequence is $a_n=1.01a_{n-1}$ .

  $a_1=01.01$

The given options are:

1. 58.65
2. 8.73
3. 1.08
4. 586459.38

Calculation:

The given sequence is $a_n=1.01a_{n-1}$ .

Therefore, $r=1.01$

Now, according to the question of $a_1=-5$ . Therefore,

  $\begin{array}{l}{a}_n=a_1{r}^{n-1}\\ \Rightarrow a_n=1.01{\left(r\right)}^{n-1}\left\{\text{substitutes these value}\right\}\\ \therefore a_n=1.01{\left(1.01\right)}^{n-1}\end{array}$

Therefore, the 873rd term of the sequence is

  $\begin{array}{l}{a}_{873}=1.01{\left(1.01\right)}^{873-1}\\ a_{873}=1.01{\left(1.01\right)}^{872}=58.65\end{array}$

Hence, the explicit rule for the given sequence is $a_{873}=58.65$ .

Therefore, the correct option is (A).