Question

Decide whether the sequence is an arithmetic, Geometric, or neither. Explain your answer.

6,24,96,384

Answer 1

@Calcmathlete

Answer 2

what does arithmetic and geometric mean?

Answer 3

i think the answer would be arithmetic?

Answer 4

Well, arithmetic sequences have a common difference. So if \(a_2 - a_2\) remains constant when doing \(a_3 - a_2\) and so on, it's arithmetic.
Geometric sequences have a common ratio. So if \(a_2/a_1\) remains constant when doing \(a_3/a_2\) and so on, then it's geometric. If it's neither of these, then it's neither.

Answer 5

So what do you think it is?

Answer 6

i dont understand ur definition.

Answer 7

what is a2-a1

Answer 8

\(a_2\) is the second term of the sequence.

Answer 9

Let's see if looking at an example will help.
1, 2, 4, 8, 16...
This is a geometric sequence.
1, 2, 3, 4, 5, 6, 7...
THis is an arithmetic sequence.

Answer 10

and what do you mean by "if a2−a2 remains constant when doing a3−a2"

Answer 11

So let's take a look.
\[a_2 - a_1 \implies 24 - 6 \implies 18\]Now let's do \(a_3 - a_2\)
\[a_3 - a_2 \implies 96 - 24 \implies 72\]\[18 ≠ 72\]

Answer 12

Therefore, it's not an arithmetic sequence.

Answer 13

Now let's test to see if it's a geometric sequence.
\[a_2/a_1 \implies 24/6 \implies 4\]\[a_3/a_2 \implies 96/24 \implies 4\]\[4 = 4\]Therefore, it's a geometric sequence. Get it?

Answer 14

where did u get 24 from?

Answer 15

24 is the second term in the sequence.

Answer 16

oh ok rite MY SEQUENCE not ur example

Answer 17

lol yeah.

Answer 18

wait why did u do a2-a1. is that the formula?

Answer 19

THat's just how you can test for the common difference. You can honestly do that for any of the terms as long it's a term - the term previous.

Answer 20

Honestly though, you can see just by looking at a sequence if it's geometric or arithmetic.
For instance. If I gave you the choice to say arithmetic or geometric for the following sequence, which one would you think?
1, 5, 25, 125, 62...

Answer 21

sry can u plz explain those same steps again my copy and pasting

Answer 22

@Topkart33 com here

Answer 23

Alright. To find a common difference which can also test to see if the sequence is arithmetic, just do \(a_2 - a_1\) or \(a_3 - a_2\) or \(a_4 - a_3\) and so on...
To find a common ratio which can also test to see if the sequence is geometric, just do \(a_2/a_1\) or \(a_3/a_2\) and so on...Once you get used to working with series and sequences, you'll do this instinctively.

Answer 24

what's the common difference?

Answer 25

You mean a definition?

Answer 26

yeah

Answer 27

calcmath u still there? plz dont give me a link unless it has pictures to explain

Answer 28

Alright. A common difference is a number in arithmetic sequences that when added to terms of the sequence gives you the following term.

Answer 29

so it's only in arithmetic sequences? I dont understand that definition

Answer 30

and what terms are you talking about in ur definition?

Answer 31

It's only in arithmetic sequences. Terms are the numbers in a sequnce or series. In your sequence, the terms are 6, 24, 96, 384

Answer 32

what do u mean by following term in your definition?

Answer 33

Alright. A common difference is a number in arithmetic sequences that when added to terms of the sequence gives you the following term.
/i\
i
i
what is the following term?

Answer 34

The term that comes after what you added the term to.
If I add the common difference to \(a_1\), then you should get \(a_2\).

Answer 35

ok what's the common difference in my sequence: 6,24,96,384

Answer 36

calcmath...hello?

Answer 37

I am here. There is no common difference there since the sequence is geometric...

Answer 38

ok now next question:
-11, -7,-3,1,.....

Answer 39

I will answer it

Answer 40

u tell me if its right of wrong only

Answer 41

is it arithmetic?

Answer 42

Yup. What do you think the common difference is?

Answer 43

idk? can u show me?

Answer 44

calc

Answer 45

Do you at least have a guess?

Answer 46

no I dont know how to figure it out. my guess is -4

Answer 47

It would be a positive 4.
\[-7 - (-11) = 4\]\[-3 - (-7) = 4\]\[1 - (-3) = 4\]See? They all say that it's 4 :)

Answer 48

ok thx can you plz stay on this chat cause I am going to answer more questions and I need you to check it for me then I need help on other questions.

Answer 49

-3/5, 4/25, 5/125, 6/625

Answer 50

Alright.

Answer 51

dont anwer it

Answer 52

I will answer it, you will check my answer :) ?

Answer 53

not to be rude...

Answer 54

np :)

Answer 55

Well...

Answer 56

is it neither?

Answer 57

It took alwhile becasue I was working it out

Answer 58

Yup. It's neither.

Answer 59

when I am not typing, dont think that I am not on :D I am always on. I think it's rude to leave someone waiting for you

Answer 60

Yeah...if I don't respond in under a minute, I'm still here, so don't freak out lol

Answer 61

alright next question:
4, 13, 22, 31

Answer 62

is it arithmetic?

Answer 63

Yes. And the common difference?

Answer 64

9

Answer 65

Yes!

Answer 66

YAY! next question:
1/3, 2/3, 1, 4/3

Answer 67

is it arichmetic?

Answer 68

Yes.

Answer 69

alright and common difference is 1/3

Answer 70

umm calc?

Answer 71

calc?

Answer 72

Yes. You are correct.

Answer 73

alright next

Answer 74

Find the common ratio of the geometric sequence.

3, 6, 12, 24

Answer 75

What do you think?

Answer 76

Do you know how to do it?

Answer 77

i dont know how to do it?

Answer 78

Alright.
\[6/3 = 2\]\[12/6 = 2\]\[24/12 = 2\]

Answer 79

umm so the common ratio is 2?

Answer 80

Yes.

Answer 81

oooh

Answer 82

ok next question.

5, 40, 320, 2560, ....

Answer 83

Can you try this one?

Answer 84

YES WAIT i AM DOING IT :D

Answer 85

8?

Answer 86

Yup :)

Answer 87

alright next:
-1/4, 1/8, -1/16, 1/32

Answer 88

-1/2

Answer 89

Yup :)

Answer 90

alright thx next:
Find the 10th term and write a rule for the nth term of the geometric sequence then find asub6:

6, -30, 150, -750

Answer 91

Are you familiar with these?

Answer 92

nope how do I do them?

Answer 93

Ok. For these, first find what the common ratio is.

Answer 94

-5

Answer 95

Ok. Now are you familiar with the formulas \[a_n = a_1 + (n - 1)d\]and\[a_n = a_1r^{n - 1}\]

Answer 96

I remember those now but need help using them

Answer 97

what is the d, n, and r

Answer 98

d = common difference
r = common ratio
n = number of terms