Chapter 6.6, Problem 39E

a.

To determine

To write a function that represents the sequence of figures.

Answer to Problem 39E

  $f\left(n\right)=\left(1\right){\left(9\right)}^{n-1}$

Explanation of Solution

Given information :

  

Number of boxes in given figures are,

1 , 9, 81 . . .

We know the sequence is in geometric progression, hence $f\left(n\right)=a_1{r}^{n-1}$

Put the values given,

  $a=1,r=9$

We get,

  $f\left(n\right)=\left(1\right){\left(9\right)}^{n-1}$

b.

To determine

To determine number of boxes in 10^th figure.

Answer to Problem 39E

There shall be 387420489 boxes.

Explanation of Solution

Given information :

  

In part a, we get,

  $f\left(n\right)=\left(1\right){\left(9\right)}^{n-1}$

Now we shall put $n=10$ we get,

  $f\left(10\right)={\left(9\right)}^{10-1}=387420489$

Hence there shall be 387420489 boxes.