Question

GEOMETRIC SEQUENCES
A ball is dropped from a height of 12 feet and returns to a height that is one-half of the height from which it fell. The ball continues to bounce half the height of the previous bounce each time. How far will the ball have traveled when it hits the ground for the fifth time?

Answer 1

@eliesaab

Answer 2

h -> 1/2 h -> (^1/2)2 h->(1/2)^3 h ->(1/2)^4 h etc

Answer 3

let us call \( a =\frac 1 2\) and \( h=12\)

Answer 4

the first time it bounces it travels h, the second times it hits, it will have traveled
\[
h + a h +a h\]

Answer 5

the second times it hits, it will have traveled
\[
h+ a h + ah + a^2 h + a^2 h
\]

Answer 6

the fifth times it hits it would have traveled\[
h + 2 ah + 2 a^2 h + 2a^3h + 2 a^4 h + 2 a^5 h
\]

Answer 7

are you following me?

Answer 8

\[
h + 2 ah + 2 a^2 h + 2a^3h + 2 a^4 h + 2 a^5 h\\
h( 1 + 2a( 1 + a +a^2 +a^3 +a^4))\\
\]

Answer 9

\[
1 + a +a^2 +a^3 +a^4
\]
Do you know how to find the sum of a geometric series?
http://openstudy.com/study#/updates/5807f8b1e4b012711f1652b2

Answer 10

I've never heard of this formula, sorry I left for a little to help my sister with her school

Answer 11

@eliesaab i'm back

Answer 12

is it 1.5 feet? @Directrix @Aleah54 @eliesaab @Kikuo @umerlodhi @YourBoyDusty @green @Living4Jesus @Astrophysics @pooja195

Answer 13

I'm pretty sure its .375 feet. For instance

For a mathematical way, you can say
\[an= an_{-1} /2 --- a1=12\]