Question

Find an equation for the nth term of the sequence.

-3, -12, -48, -192, ...

Answer 1

have you found the common ratio?

Answer 2

http://openstudy.com/users/abbs__#/updates/5654d0a2e4b0959c2b13a479 I have discussed this question in much detail
you never asked any questions

Answer 3

well what do you see the numbers are doing each time ?

Answer 4

sorry i did not see you commented on it

Answer 5

its okay tell me what you think is happening ?

Answer 6

and i see the numbers being multiplied by 4

Answer 7

right that is your common ratio r=4

Answer 8

yes so how would you get the ninth number ?

Answer 9

so now just notice your first term in plug into the form I had for your nth term

Answer 10

how do i figure out whats the ninth number?

Answer 11

we first you can keep multiplying the numbers until you get there

Answer 12

so 192x4=768
768x4=3072
3072x4=12288
12288x4=49152
49152x4= your answer

Answer 13

oh so the ninth number will be the ninth number is 296,608

Answer 14

the formula for the nth term in a geometric series is \(a_n=a_1*r^{n-1}\)

Answer 15

no retype that

Answer 16

i meant 196,608 sorry

Answer 17

yes

Answer 18

even if they asked for the ninth term that is incorrect what you guys have as the ninth term

they are looking for the nth term which is what I have tried to express to you the other day @Abbs__ and what @bibby is now telling you

Answer 19

oh, I didn't read the directions, I thought we wanted the 9th term lol

Answer 20

oh me too

Answer 21

I am very confused now

Answer 22

you are just missing negative sign on your ninth term

Answer 23

you need to identify the common ratio r which is 4
and the first term a1 which is -3
and just plug into the nth term of the sequence which is:
\[a_n=a_1 \cdot r^{n-1}\]

Answer 24

so it will be an=-3x4^n-1 ?

Answer 25

aka an=-12^n-1 ?

Answer 26

yes to the first answer
and no the second thing you wrote is not equivalent
if you notice that is what @rebeccaxhawaii did above:
\[\text{ ninth term }=a_9= =a \cdot r \cdot r \cdot r \cdot r \cdot r\cdot r\cdot r \cdot r=a r^{8}=a r^{9-1}\]

Answer 27

oh okay i get it, thankyou! :)

Answer 28

\[a_n=-3 \cdot 4^{n-1} \text{ which is correct }\]