Question

The second term in a geometric sequence is 50. The fourth term in the same sequence is 112.5. What is the common ratio in this sequence?

Answer 1

also I would appreciate it if you can give me the answer to this question.

Answer 2

geometric sequence: \(a_n = a_1r^{n-1}\)

Answer 3

ok so whats the final answer?

Answer 4

One moment.

Answer 5

ok

Answer 6

what math are you in?

Answer 7

Algebra 2

Answer 8

lazy lazy lazy
you make me sick
how about putting some effort into the process of LEARNING?

Answer 9

please go troll somewhere else nubby Unlike it's really urgent for me to get this answer.

Answer 10

You just want an answer. This isn't trolling it's an unhealthy attitude

Answer 11

Jhan is completely wasting her time on some gutter trash like yourself when you won't even read her explanation

Answer 12

I need to compare my answer to her and you are seriously not helping by using such degrading comments.

Answer 13

post your answer and show your work. that's how it works on stackexchange, that's how it should work here

Answer 14

You seriously think we haven't heard these excuses 100 time`s before?

Answer 15

here is a link to someone else who had the same problem

http://openstudy.com/study#/updates/530596b6e4b022471a6500d8

Hope it helps

Answer 16

Thanks but what I need is the answer so I can check if mine is correct.

Answer 17

what's your answer you shmuck

Answer 18

\[a_1r^{2-1}=50~,~ a_1r^{4-1} = 112.5\] \[a_n=a_1r^{n-1}\] \[a_1r^{2-1} =a_1r=50\]\[a_1r^{3-1} = a_1r^2 \]\[a_1r^{4-1} = a_1r^3=112.5\] \[a_1=\frac{50}{r}\]\[a_1=\frac{112.5}{r^3}\]Since it is part of the same sequence, you can solve for \(a_1\) for both of these, and set the ratios equal to eachother and solve for \(r\). \[\dfrac{\dfrac{50}{r}}{\dfrac{112.5}{r^3}}=a_1\]

Answer 19

\[a_1: \frac{50}{r}=\frac{r^3}{112.5}\]\[r^4=(50\cdot 112.5)\]\[r=\sqrt[4]{5625}\]\[r=(5625)^{1/4}\]

Answer 20

I think if it was part of a different sequence, you would not be able to set the ratios equal to eachother because you would have to infer that \(a_1\) might be different.

Answer 21

well I did do it that way and I got 1.5 but I don't know if it is correct

Answer 22

Can you show how you got 1.5?

Answer 23

If you solve for that, \(r\approx 8.66\)

Answer 24

oh would that be the final answer then?

Answer 25

Do you have answeer choices you can check with? I'm curious how you got 1.5.

Answer 26

I multiplied the 50 and 112.5 then divided and got 75 which is 3/4

Answer 27

divided by what?

Answer 28

nvm thanks for helping

Answer 29

Hmm.. ok, np.