Question

Need help understanding number 2.

Answer 1

I don't understand the formula, what does each variable represent?

Answer 2

\(a_1\) is the first number \(r\) is the common ratio (what you multiply one by to get the other) and \(n\) is the number of terms

Answer 3

The terms I'm left with after I figure out the common ratio?

Answer 4

lets to it by example for the first ball

Answer 5

2.4/3

Answer 6

\[a_1=3\\
r=\frac{2.4}{3}=.8\]

Answer 7

New divided by the old.

Answer 8

\[a_5=3\times .8^4\]

Answer 9

right

Answer 10

Wait I was never tolled to times the first number by the number of ratios.

Answer 11

\[a_1,a_2,a_3,a_4,a_5,a_6\\
a_1,a_1r,a_1r^2,a_1r^3,a_1r^4,a_1r^5\]

Answer 12

O_O that's how the flvs Algebra II lesson looks like? :O

Answer 13

So in the end will Ball 1 be 1.04? I got that from Dividing the old by the new.

EX: 2.4/3, 1.9/2.4, 1.5/1.9, 1.2/1.5 then add them together, and divide by 4.

Answer 14

Yeah @tHe_FiZiCx99.

Answer 15

It's easy it's just I tend to come to things that I over look or think way too hard about when it turns out to be incredibly simple; or they explained it badly.

Answer 16

@satellite73 when you're ready.

Answer 17

Um to find the ratio you divide, why did you add and divide by 4?

Answer 18

Well that's what happens when you ask the wrong people for help in school. ^^'

Answer 19

So just divide then times it by the top?

Like how satellite73 showed?

Answer 20

I'm familiar with this however they're asking for a common ratio between the 2, i sort of remember how to find it. Not too sure though, I can easily do the 2 and 3rd.

I think i might know how to find it :/

Answer 21

Alrighty, getting kind of confused due to the fact that I've been going about it some what wrong. What would Ball 1 end up being?

Answer 22

The ratio for ball I?

Answer 23

Yes.

Answer 24

2.4 / 3 = 0.8
1.9 / 2.4 = 0.79 rounded to 0.8
1.9/1.5 = 0.789 rounded to 0.8 and so on...

a_1 = the first term so 3

a_n = a_1 * r^n-1
a_n = 3 * 0.8^n-1

Answer 25

Oh snap I'm getting it. ^_^ Alright, can I call you back to check if I'm doing correctly for Ball II?

Answer 26

sure

Answer 27

common ratio, hm, i don't know how to answer that one :/

Answer 28

1.9/3= 0.63 round = 0.6
1.2/1.9= 0.63 round = 0.6
0.8/1.2= 0.66 round = 0.7

Would this have it's own a_n = a_1 * r^n-1 equation?

Answer 29

Each ball has it own equation.

Answer 30

Cool. 1 minute...

Answer 31

Would it be
a_n= 1.9 * 0.6^n-1?

Answer 32

a_1 = the first term

Answer 33

So it will constantly be 3.

Answer 34

a_n = 3 * 0.6^n-1

Answer 35

a_n = 3 * 0.6^n-1
-----------------

a_6 = 3 * 0.6^6-1

a_6 = 3 * 0.6^5

a_6 = 3 * 0.07776

a_6 = 0.23328

Though its asking for the fifth bounce, it says to use height 6... that should technically be:

a_5 = 3 * 0.6^5-1

a_5 = 3 * 0.6^4

a_5 = 3 * 0.1296

a_5 = 0.3888

Answer 36

It's adding 1 to it for some reason, the equation is correct --lease I'm pretty sure it is,

Find the 3rd height, that would be 0.6^2 = 0.36 * 3 = 1.08 = 1.1... in your table it says 1.2. It does that for everyone of them ._.

Answer 37

Why am I squaring 0.6 by two for the 3rd height?

Answer 38

because its ^n-1

if its for the 5th term it would be from a_N to a_5

r^N-1 --> r^5-1 -> r^4

Answer 39

Alright.

Answer 40

Get it?

Answer 41

So when trying to find the fifth bounce it would be to the fourth power?

Answer 42

yes because its n-1

Answer 43

So why did they say height six when trying to find the fifth bounce? lol They added 1 instead of subtract.

Answer 44

I'm not sure, I'm in algebra I and I've found so many typos in my lesson -- also go to flvs :/ I've actually asked them on here to see lol

Answer 45

lol

Answer 46

Maybe they were referring to using 6 because 6-1 = 5 and they're looking for the successive bounce. Though using 6 would mean find the 6th bounce because of the nth term. That would be a_6

Answer 47

The typos get worse, I've seen many Algebra 2 questions on here from FLVS which couldn't have been answered because of that.

Answer 48

Lol ikr, I should get credit for reporting them, too mcuh work and stuff :/

Answer 49

Yeeaah, I'm going to ignore 6.

Answer 50

Explain why you didn't use 6 so you get credit for trying if anything lol xD

Answer 51

They're trying to refer it as an example. Yeah for real. lol

Answer 52

I got that from the point they used "i.e"

Answer 53

Yeah. Hold up, trying to solve this once and for all. :)

Answer 54

kk

Answer 55

Ball 2's formula should look like this right? a_4 = 3 * 0.6^4-1

Answer 56

yes

Answer 57

Wait it should be a_4 = 3 * 0.6^5-1

Then a_4 = 3 * 0.6^4

Answer 58

Because we're solving for the fifth bounce.

Answer 59

Nope, you're trying to find the 4th bounce right?

Answer 60

For the fifth bounce that would be a_5 = 3 * 0.6^5-1

Answer 61

Fifth lol Doing question 2 Cool just caught myself on that.

Answer 62

It's asking for EACH ball, find the fifth bounce for ball I, II and III

Answer 63

a_4 = 3 * 0.1296

0.1296 round 0.1?

Answer 64

why're you doing a_4?

Answer 65

a_4 = 3 * 0.6^5-1
V
4

Answer 66

Yes, why a_4 though?

Answer 67

Crap a_5 = 3 * 0.6^5-1
V
5

Answer 68

Ugh! a_5 = 3 * 0.6^5-1
V
4

Answer 69

There. o_0 Darn small keyboard.

Answer 70

I'm solving for the fifth bounce, so minus one, left with four.

Answer 71

yes, A_5 = 3 * 0.6^5-1 = a_5 = 3 * 0.6^4

Answer 72

My bad I forgot to change a_4 = to a_5 =

Answer 73

So I'm left with a_5 = 0.3?

Answer 74

3_5 = 0.3

Answer 75

0.4 rounded

Answer 76

Since a is 3

Answer 77

X_X I am completely lost on what you're doing

Answer 78

No I was talking about the first a, "a_5 = 3 * 0.1296"
^

Answer 79

It's all good. I get what you're saying. ^_^

Answer 80

kk find the fifth bounce for all 3 balls

Answer 81

Alright. ^w^

Answer 82

Will take a while so sit back and relax. 'u'

Answer 83

Lol i have to get off soon >.>

Answer 84

It's alright do your thing, you've done your part now it's up to me to do mine. ;) Thank you so much! Goodnight.

Answer 85

I'm doing my own assignment lol, I'll be on my other tab xD I'll be looking back every 15 ish minutes or so :p

Answer 86

K :)

Answer 87

Ball 1: 3_5 = 3 * 0.8^5-1
3 * 0.8^4
3_5 = 3*0.4
3_5 = 1.2

Answer 88

What do I do with 3_5? Feels like I'm suppose to simplify it.

Answer 89

What do I when I get one different?

Ball 3: 0.3
0.3
0.3
0.2

Answer 90

3_5 = 3 * 0.3^5-1
3*0.3^4
0.0081
3_5 = 0.02

Answer 91

3_5 ????

Answer 92

a_n = a_1 * r^n-1
3_5 = 3_1 * 0.3^5-1

Answer 93

3, where did it come from?

Answer 94

Ahhh, i get what you did, not you just use a_5

Answer 95

Okay. :)

Answer 96

Ball 1: a_5 = 3 * 0.8^5-1
3 * 0.8^4
a_5 = 3*0.4
a_5 = 1.2


Ball 2: a_5 = 0.4


Ball 3: 0.3
0.3
0.3
0.2
a_5 = 3 * 0.3^5-1
3*0.3^4
0.0081
a_5 = 0.02