Chapter 8.3, Problem 60E

a.

To determine

To find: The rule for the number of skydiver in nth ring of the given sequence.

Answer to Problem 60E

  $a_n=5{\left(2\right)}^{n-1}$ .

Explanation of Solution

Given information:

In the skydiving ring formation with R rings, each ring after first has twice many skydivers as the preceding rings. First ring has $5$ skydivers.

Calculation:

In the skydiving ring formation with R rings, each ring after first has twice many skydivers as the preceding rings. First ring has $5$ skydivers.

i.e. $a_1=5,r=2$ .

General rule for nth term of a geometric series is given by-

  $a_n=a_1{r}^{n-1}$

Substitute $a_1=5,r=2$ ,

Therefore the rule for nth term of given geometric series would be given by −

  $a_n=5{\left(2\right)}^{n-1}$ .

b.

To determine

To find: The total number of skydivers when there are four rings.

Answer to Problem 60E

  $75$ .

Explanation of Solution

Given information:

Same as part $a$ of this exercise.

Calculation:

From part $a$ of this exercise-

  $a_1=5,r=2$ , $a_n=5{\left(2\right)}^{n-1}$

Using sum formula for geometric progression,

  $\begin{array}{l}{S}_n=a_1\left(\frac{1-r^n}{1-r}\right)\\ \text{Substitute }n=4,a_1=5,r=2\\ S_4=5\left(\frac{1-{\left(2\right)}^4}{1-2}\right)\\ \Rightarrow S_4=5\times 15\\ \Rightarrow S_4=75\end{array}$

Hence, total number of skydivers in four rings would be $75$ .