Question

what is the next term in the geometric sequence 6, -4, 8/3, -16/9

Answer 1

compare the terms to find the common ratio

does

\[\frac{-4}{6} = \frac{-4}{\frac{8}{3}}\]

if it does then you have the common ratio... r

so the next term will be

\[\frac{-16}{3} \times r\]

hope it helps

Answer 2

how did you find that i mean did you solve the ratio?

Answer 3

what is r

Answer 4

just see if

both simplify to the same value

oops and the 2nd ratio should be

\[\frac{\frac{8}{3}}{-4}\]

Answer 5

r is the common ratio....

by comparing the ratios

-4/6 and (8/3)/-4

you can find what each term is being multiplied by to get the next term

Answer 6

Oh ok I get it thank you.

Answer 7

\(\bf \cfrac{\frac{8}{3}}{-4}\implies \cfrac{\frac{8}{3}}{-\frac{4}{1}}\implies \cfrac{8}{3}\cdot -\cfrac{1}{4}\)

Answer 8

So what would the answer be because i tried it and got -16=16

Answer 9

nope.... it doesn't fit the pattern...

so start by simplifying

-4/6 what do you get..?

Answer 10

-2/3

Answer 11

great so then check the 3rd term

is 3rd term = 2 term times -2/3

which means is

\[\frac{8}{3} = -4 \times -\frac{-2}{3}\]

Answer 12

if it is then you've found the common ratio...

Answer 13

my options are
A.-8/3
B.-32/27
C.32/27
D.8/3
E.106/9

Answer 14

\(\large \begin{array}{ccccc}
6&-4&\frac{8}{3}&-\frac{16}{9}\\
\hline\\
&\qquad 6\cdot {\color{red}{ -\frac{2}{3}}}&\qquad -4\cdot {\color{red}{ -\frac{2}{3}}}&\qquad \frac{8}{3}\cdot {\color{red}{ -\frac{2}{3}}}
\end{array}\)

Answer 15

so... what do you think is next?

Answer 16

B.-32/27
C.32/27 right?

Answer 17

well. what did you get?

Answer 18

32/27

Answer 19

that's what i got

Answer 20

the idea of a sequence is that, the NEXT term, depends on whatever the PREVIOUS term is
so you grab the PREVIOUS term and multiply it by some value, that is the "common ratio"

Answer 21

Thank you

Answer 22

\(\large \begin{array}{ccccc}
6&-4&\frac{8}{3}&-\frac{16}{9}&{\color{blue}{ \frac{32}{27}}}\\
\hline\\
&\qquad 6\cdot {\color{red}{ -\frac{2}{3}}}&\qquad -4\cdot {\color{red}{ -\frac{2}{3}}}&\qquad \frac{8}{3}\cdot {\color{red}{ -\frac{2}{3}}}&\qquad -\frac{16}{9}\cdot {\color{red}{ -\frac{2}{3}}}
\end{array}\)

32/27 \(\large \checkmark\)

Answer 23

There we go thank you again

Answer 24

yw