Question

How do I find the common ratio with this data?

Ball 1 height - 8ft, 5 1/2ft, 4ft, 2ft, 3/4ft
Ball 2 height - 8ft, 5 3/4ft, 4 1/3ft, 2 1/2ft, and 1 ft
Ball 3 height - 8ft, 5 1/3 ft, 4 1/4ft, 2 1/3ft, 1 ft

Answer 1

@antoni7

Answer 2

PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 3

generally the common ratio is found by : the first term divided by the second term

Answer 4

you got no idea how to do this ?

Answer 5

So I divide 5 1/2 by 4 ft?

Answer 6

yes...

Answer 7

and i divide 2ft and 3/4ft?

Answer 8

sorry if this is an obvious question...

Answer 9

ball 1 height : common ratio = 8/ 5 1/2
ball 2 height : common ratio = 8 / 5 3/4
ball 3 height : common ration = 8 / 5 1/3

Answer 10

do i divide those?

Answer 11

you ll obtain the common ratio of each balls height...

Answer 12

so is that a yes?

Answer 13

yeah... what im confused about is the question ... does it ask you for each ball height common ratio ?

Answer 14

yes

Answer 15

i found my answers by dividing

Answer 16

common ratio is usually denoted by " r "
So r for ball height 1 = 16/5
height 2 = 32/15
height 3 = 24 /5

Answer 17

so do i divide those?

Answer 18

i divided the ones you showed me previously

Answer 19

yup i just wrote the answers..

Answer 20

thank you

Answer 21

just inform me if you got these answers right or wrong

Answer 22

I definitely will.

Answer 23

ok good luck :) Enjoy studying

Answer 24

Do you think the common ratio would affect the size of the ball?

Answer 25

I don't see how it would...?

Answer 26

For Geometric sequences
suppose you got a sequence : 2, 4, 16 , 64
the first term would be denoted as " a" and where a = 2
the common ratio , r = 4 divide 2 = 2
the general form , Tn = ar^ (n-1)
Tn = 2 x 2 ^ ( n-1)

suppose you want to know the 3rd term of the sequence
T3 = 4 ^ (3-1) = 4 ^ 2 = 16

Answer 27

so yes....?

Answer 28

im confused by your example

Answer 29

the common ratio is something which is constant..

Answer 30

for a specific sequence the common ratio stay the same..

Answer 31

oh alright:) wow thanks

Answer 32

can you help me go through this other step please

Answer 33

sure but i'm not 100% right about the answers i'm giving you... you need to check it out later with your teacher ....

Answer 34

If ball 1 were dropped from 2 feet higher, would the common ratio be different? Explain your answer.


I think it would because you'd be adding 2 feet more to the equation

Answer 35

yeah i guess so

Answer 36

10 ft divide by 8 common ratio , r = 10 / 8 = 1.25

Answer 37

wheareas 8 ft divide by 5.5 ft , r = 8 / 5.5 = 1.45

Answer 38

What is the height of each ball on the fifth bounce (i.e., Height 6)? Use the geometric sequence formula, an = a1rn – 1 and show your work.


an is the last term
a1 = 1st term
r = ratio
n = # of terms in a finite sequence

Answer 39

What numbers would I use to plug in?

Answer 40

there were 3 balls

Answer 41

T6 = first term x (common ratio of ball 1height )^ ( 5)

Answer 42

T6 = first term x (common ratio of ball 2height )^ ( 5)
T6 = first term x (common ratio of ball 3height )^ ( 5)

Answer 43

thank you.... oh my god thank you thank you thank you

Answer 44

where do i find the 1st terms though?

Answer 45

one quick question

Answer 46

where do i find the ball height? are they talking about the very first one in the data i provided?

Answer 47

first term = 8 ft

Answer 48

8ft x 3.2 x ___________?

Answer 49

a1 x ratio x height of 1^5

Answer 50

whats the height of 1, 2, and 3?

Answer 51

its the first term of each ball that is ball 1 = 8ft ball 2= 8ft ball 3 = 8ft

Answer 52

wait huh?

Answer 53

i just use 1 for the first height, 2 for the second height, and 3 for the third?

Answer 54

wait wait "confused" what is the question ?

Answer 55

what I use is: a1 x ratio x "ball height" 1^5

but what do i plug in for "ball height"?

Answer 56

the ball height is 8ft right ?

Answer 57

yes

Answer 58

that's the first term (a1)

Answer 59

T6 = first term x (common ratio of ball 1height )^ ( 5)
= (8 x 3.2 )^5
T6 = first term x (common ratio of ball 2height )^ ( 5)
= (8 x 2.13333 )^5
T6 = first term x (common ratio of ball 3height )^ ( 5)
= (8 x 4.8 ) ^ 5

Answer 60

its the answer for the question :
What is the height of each ball on the fifth bounce (i.e., Height 6)? Use the geometric sequence formula, an = a1rn – 1 and show your work.


an is the last term
a1 = 1st term
r = ratio
n = # of terms in a finite sequence

Answer 61

ohhhh!!!!!!!!!!!!!! so what threw me off was the height

Answer 62

thank you!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 63

done with this awesome question on geometric series ?

Answer 64

yes thank god

Answer 65

but i literally have one more question that deals with all of this

Answer 66

I have to find the total distance of the height each ball was traveled using a specific formula