Chapter 9.8, Problem 32PPS

(a)

To determine

A formula for nth term of the geometric sequence

Answer to Problem 32PPS

  ${\left(1.2\right)}^n$

Explanation of Solution

Given:

Mr. Mosley notice that when he clicks a spot on the map, the map zooms in on that spot. It increases by 20%

  $r=1.2$

Concept Used:

The equation for nth term is $a_n=a_1{\left(r\right)}^{n-1}$

The ratio is given by the formula

  $r=\frac{a_2}{a_1}=\frac{a_3}{a_2}$

Calculation:

In order to find the formula as shown below:

  $a_n={\left(1.2\right)}^n$

Thus, the formula is $a_n={\left(1.2\right)}^n$

(b)

To determine

Fourth term of sequence

Answer to Problem 32PPS

  $a_4=2.0736$

Explanation of Solution

Given:

Mr. Mosley notice that when he clicks a spot on the map, the map zooms in on that spot. It increases by 20%

  $r=1.2$

Concept Used:

The equation for nth term is $a_n=a_1{\left(r\right)}^{n-1}$

The ratio is given by the formula

  $r=\frac{a_2}{a_1}=\frac{a_3}{a_2}$

Calculation:

In order to find the formula as shown below:

  $\begin{array}{l}{a}_n={\left(1.2\right)}^n\\ a_4={\left(1.2\right)}^4\\ a_4=2.0736\end{array}$

Thus, the formula is $a_4=2.0736$ .