Question

A ball is dropped from the height of 475 centimeters. Each time it hits the floor, it rebounds to a height that is %24, percent of the previous height. Find the total distance traveled by the ball.

Answer 1

This can be represented by an infinite geometric series

Answer 2

yes can you please help me figure out how to make it a infinite geometric series

Answer 3

on each bounce it travels same distance up and down so the common ratio will be 2*0.24 = 0.48

First term will be 465 so the series is

465, 465*0.48, 465*0.48^2...

Answer 4

and the sum to infinity = a1
------
1 - r

where a1 = first term and r = common ratio.

Answer 5

wouldn't the first term be 475

Answer 6

yes 475 Typo

Answer 7

so how would i find the total distance the ball traveled @welshfella

Answer 8

total distance = sum to infinity ( the formula in my last post)

Answer 9

just plug in a1 = 475 and r = 0.48

Answer 10

\[\frac{ a1 }{ r }\]

Answer 11

no a1 / (1 - r)

Answer 12

sorry i forgot the 1-r

Answer 13

so the sum should be 913.461

Answer 14

yes

Answer 15

round it to tenths
913.5