Question

Help with geometric series?

Answer 1

What is the average common ratio between the successive height values of ball 1? Ball 2? Ball 3?

Answer 2

@jim_thompson5910 @Nnesha @wio

Answer 3

@nincompoop @TuringTest

Answer 4

to find the ratio you can divide next term by previous one
for example \[\huge\rm r = \frac{ a_2 }{ a_1 } , \frac{ a_4 }{ a_3 }\]

Answer 5

So 2.4 / 3 ?

Answer 6

And then 1.9 / 3?

Answer 7

And then 0.9 / 3?

Answer 8

for every ball you can divide height 2 by height one
any term just divide by previous term

Answer 9

yes right

Answer 10

Okay so the ratios are .8, .63, and .3.

Answer 11

Okay, next (there's only three questions) . . .

What is the height of each ball on the fifth bounce (i.e., Height 6)? Use the geometric sequence formula, \[a_{n}=a_{1}*r^{n-1}\] and show your work.

Answer 12

I think ball 1 is \[a_{6}=(3.0)(0.8^6-1)\]

Answer 13

I think I have ball 2 too but is that right?

Answer 14

I think ball 1 is \[a_{6}=(3.0)(0.8^{6-1})\]
if you meant like this then yes

Answer 15

Oh yes I did actually!

Answer 16

:-) yeah solve that
and height of each "EACH" BALL so yeas

Answer 17

Okay, then I would solve that. As for ball 2 and 3....

Ball 2: \[a_{6}=(3.0)(0.63^{6-1})\]

Ball 3:\[0.9=3r^{2-1} . . .r=0.3 . . . a_{6}=(3.0)(0.3^{6-1)}\]

And of course I would solve all of those. I just want to make sure I'm on the right path!

Answer 18

explain last one ball 3
what is .9 ?

Answer 19

Height 2=0.9

Answer 20

Yep

Answer 21

ohh you already found our r for ball 3
which is .3 i don't why you used geometric formula to find r again by replacing a_n by .9
anyways ye that's right you can just use same formula like you used for ball 2 and 1 replace r by .3 first term is 3 n = 6 that's it

Answer 22

Okay got it. Thank you so much!

Answer 23

my pleasure :-)

Answer 24

Ohh I basically just found the ratio twice here. Not sure why. I've been staring at a screen for too long.

Answer 25

:P