Question

HOW DO I FIND THE AVERAGE COMMON RATIO OF A GEOMETRIC SERIES.

Answer 1

if its a geometric sequence we have the setup:

\[g,~gr,~gr^2,~gr^3,...\]
\[\frac{gr^k}{gr^{k-1}}=r\]

Answer 2

in other words, just take some term, and divide it by the term before it ...

1,3,9,18,

3/1 = 3
9/3 = 3
18/9 = 3
etc ....

Answer 3

hmmm, that seems a bit more complicated :)

Answer 4

yeah. :/ @amistre64

Answer 5

a ratio a:b can be considered a fraction a/b

an average is a sum divided by how many there are ....

one idea may be that you can add up 5 ratio amounts and divide by 5 ... naybe

Answer 6

or, if we are trying to get a geometric sequence that starts at 3 and ends at 1.2 in 5 terms ...

Answer 7

yes, i have 5 terms, the first number is 3, and the last number is 1.2.

i need to know what the average common ratio of that is.. i dont understand how to get it.

Answer 8

\[g_n = g_{n-1}~r\]
\[g_n = g_{0}~r^{n-1}\]
\[1.2 = 3~r^{4}\]
divide and 4rt

Answer 9

or work some logs

Answer 10

@chell: Please post your own question separately. Type it into the "Ask a question" box.

Answer 11

@amistre64 okay.
so 1.2 = 3 r^4
and solve that? and that's my common ratio?

Answer 12

if we are wanting to form a geometric sequence that starts at 3, and the 5th term is 1.2 .... then yes

Answer 13

okay so that's 0.795

that's my common ratio?

Answer 14

sounds good to me .... assumptions in tow

Answer 15

to keep accuracy, 4rt(.4) might be warranted as an exact result

Answer 16

@amistre64 can you help me with this part???

Answer 17

What is the height of each ball on the fifth bounce (i.e., Height 6)? Use the geometric sequence formula, an = a1rn – 1 and show your work.
a1 = r^n-1

Answer 18

well, we know r, and the height for 5 ... so multiply r by H5 to get H6

Answer 19

what is 1.2, times 4rt(.4)?

Answer 20

1.272

Answer 21

1.2 * .795 is not more than 1.2 ....

Answer 22

79% of 1.2 is not greater than 100% of 1.2 :)

Answer 23

oh its .954 what does that have to do with this though?

Answer 24

well, 3*r^4 = 1.2 for height 5. what is height 6? tack on another r :/ ... 3*r^5

Answer 25

yes. @amistre64 that makes sense.

Answer 26

wow, i just got a notice that someone needs to learn something by today ... procrastination is such a blessing :)

Answer 27

@amistre64 thank you for your help.
i really appreciate it. (:

Answer 28

good luck ;)