Question

A bungee jumper falls 97.2 feet before bouncing back up at the end of his bungee cord. Then he falls 64.8 feet before bouncing up again. On his third descent, he falls 43.2 feet before going back up. What is the total distance the bungee jumper drops after five falls if the distances continue in this pattern? (Do not include the distance traveled up.)
234.0 ft
253.2 ft
789.8 ft
1,281.8 ft

Answer 1

Answer:

253.2 ft

Step-by-step explanation:

Given,

The distance bungee jumper drops in first fall = 97.2 feet,

In second fall = 64.8 feet,

In third fall = 43.2 feet,

......., so on, ....

Thus, the sequence that show the situation is,

97.2, 64.8, 43.2,........

Since,

$\frac{64.8}{97.2}=\frac{43.2}{64.8}=\frac{2}{3}$

⇒ The above sequence is a GP,

Having first term, a = 97.2 ft,

And, common ratio, r = 2/3,

Hence, the total distance the bungee jumper drops after five falls,

$S_{5}=\frac{a(1-r^n)}{1-r}$

$=\frac{97.2(1-(\frac{2}{3})^5)}{1-\frac{2}{3}}$

$=\frac{84.4}{\frac{1}{3}}$

$=253.2\text{ ft}$

Second option is correct.

Answer 2

This is a geometric series
To find the terms plug in the term number you are looking for as t in
An=97.2(1.5)^(t-1)

The first five terms are 97.2, 64.8, 43.2, 28.8, 19.2

add the terms together and you get 253.2feet in total