Question

Decide if the sequence is geometric. if yes, state the next 3 terms and the common ratio.

1) 6,24,96,384 ......

2) 136,68,34,17, ....

3) 1/3, 2/3, 1 , 4/3 .......

Answer 1

@jim_thompson5910
can you explain to me, im so confused on where to start

Answer 2

the first one I believe is NO

Answer 3

to figure out if it's a geometric sequence, you divide each term by the previous term

Answer 4

if you get the same common ratio every time, then it's definitely geometric

Answer 5

and once you figure out this common ratio, you use it to generate more terms

Answer 6

to find more. I have to do 34 divide by 4 ? because the common ratio is 4. or how ?

Answer 7

which one are you on?

Answer 8

#2?

Answer 9

number one. do I multiply 384 by 4 to get the next 3 terms ?

Answer 10

yes you multiply 384 by 4 to get the next term

then you multiply that term you just got by 4 to get the next term

etc etc

Answer 11

this of course only works if the sequence is geometric

Answer 12

yes yes okay ! I got it .. what if its a fraction like numbe3 ?

Answer 13

what is 2/3 divided by 1/3

Answer 14

1/3?

Answer 15

nope

Answer 16

(2/3) divided by (1/3) = (2/3)*(3/1) = ??

Answer 17

2?

Answer 18

good

Answer 19

what is 1 divided by 2/3

Answer 20

the same ?

Answer 21

you sure?

Answer 22

no ,

Answer 23

1 divided by 2/3 = (1/1)*(3/2) = ??

Answer 24

3/2?

Answer 25

good

Answer 26

so before you got 2, but now you're getting 3/2

Answer 27

this means that the ratio has changed and there is no common ratio

Answer 28

so its no

Answer 29

yep, it's not a geometric sequence

Answer 30

ok! I swear Im going to put you in my graduation speech because you've helped a lot .

Answer 31

lol I'm flattered, but I haven't helped that much really

Answer 32

glad it's all clicking though

Answer 33

ha but anyways what if they ask for the 6th term?

Answer 34

for which one

Answer 35

4) 8,2, 1/2
common ratio I found is 4 .

Answer 36

not 4, but close (sorta)

Answer 37

2/8 = ???

Answer 38

how you ge2/8

Answer 39

i picked the second term and divided it by the previous term

Answer 40

so you got 2/8 as the ratio?

Answer 41

reduce it

Answer 42

what do you get when you do

Answer 43

1/4

Answer 44

so what's what I meant when I said you were close

Answer 45

the common ratio is 1/4 and not 4

Answer 46

so to get the next term, you multiply the last term by 1/4

Answer 47

I would multiply 1/2 and 1/4?

Answer 48

multiply the numerators together

multiply the denominators together

Answer 49

1/2 times 1/4 = (1*1)/(4*2) = 1/8

Answer 50

1/8

Answer 51

yep correct

Answer 52

1/8 times 1/4 = ???

Answer 53

1/32

Answer 54

and the term after 1/32 is ???

Answer 55

128

Answer 56

not quite

Answer 57

what! it is 1/128

Answer 58

yes, so that's the sixth term

Answer 59

ok ! can you help on a word problem ?

Answer 60

sure one more

Answer 61

you got to go?

Answer 62

no but I don't want to do all your hw

although you seem far from the type that just dumps all their hw on here and doesn't bother to learn, so that's good

Answer 63

oh yes I know. I just got two more and ill do the rest by myself.

Answer 64

ok great, I don't want to discourage you from asking for help

Answer 65

I just don't want you too dependent on this site either

Answer 66

yes I understand. can I ask you something im always curious about lol

Answer 67

sure go for it

Answer 68

how old are you

Answer 69

26 why do you ask

Answer 70

just always been curious

Answer 71

i gotcha

Answer 72

I guess I don't sound like a teen huh?

Answer 73

anyways, what's your other questions (math questions lol)

Answer 74

then again, age is a number which is a math thing too, so that's partially relevant

Answer 75

you just sound or seem, well educated and well mannered lol yes hold on its long

Answer 76

hmm I guess so, but a teen could sound like it too maybe

Answer 77

so it's a word problem?

Answer 78

heavy rain in brieannes town caused the river to rise. the river rose three inches the first day. and each day after that it rose twice as much as the previous day.

what type of sequence is own in the above situation?

why is it this type of sequence?

write a rule for the nthterm of this situation?

how manydid the river rise the 7th day?

howmuch total did the river rise in five days?

Answer 79

so we basically have this sequence

3, 6, 12, 24, 48, 96, ...

ie you start with 3 and you double each term to get the next term

Answer 80

so what type of sequence is this?

Answer 81

geometric

Answer 82

how do you know this

Answer 83

doubles each term

Answer 84

so in more mathematical terms, you're basically saying the common ratio is r = 2

Answer 85

that answers the second part

Answer 86

write a rule for the nth term of this situation


first term: a = 3
common ratio: r = 2

nth term

\[\large a_{n} = a*r^{n-1}\]

\[\large a_{n} = 3*r^{n-1}\]

\[\large a_{n} = 3*2^{n-1}\]

Answer 87

so the nth term is

\[\large a_{n} = 3*2^{n-1}\]

Answer 88

how many inches did the river rise the 7th day?

plug in n = 7 and evaluate, then tell me what you get

Answer 89

36

Answer 90

that's too small

Answer 91

i got 3(2) ^6

Answer 92

that's not 36 though

Answer 93

you evaluate 2^6 first, then you multiply

Answer 94

i don't have a calculator that

Answer 95

then use google as a calculator

https://www.google.com/search?q=3%282%29+^6&ie=UTF-8

Answer 96

64

Answer 97

no it's not 64, look at the result google calculator spits out

Answer 98

at the link i sent