Question

FAN AND MEDAL. What is the 9th term of the geometric sequence where a1 = -8 and a6 = -8,192?

Answer 1

A. -327,680
B. -393,216
C. -458,752
D. -524,288

Answer 2

\[a_n = a_1 q^{n-1}\], so...
\[a_6 = a_1 q^{5}\]\[-8.192 = -8 q^{5}\]\[q = 1.00475\]
Now, just find the a_9

Answer 3

please note that:
\[a _{6}=a _{1}*q ^{5}\]whre q is the constant f yr geometric sequence

Answer 4

Do you understand?

Answer 5

oops...of your geometric...

Answer 6

No.

Answer 7

The geometric sequency have the form:
\[a_n = a_1 q^{n-1}\]

Answer 8

if we know the ratio "q" and the first element of the sequency "a_1", we can calculate any element of this sequency

Answer 9

please substitute your umerical data ino the subsequent relation:
\[a _{6}=a _{1}*q ^{5}\]
and find q^5, please!

Answer 10

you know the first element "a_1" and element "a_6", using the equation above, you need to find the ratio of the sequency, for just then, find the value of "a_9" by:
\[a_9 = a_1 q^{8}\]

Answer 11

got it?

Answer 12

I'm actually confused.

Answer 13

have u ever seen the equation i showed you?

Answer 14

In what exactly you got confused?

Answer 15

No, I don't think I've ever seen the equation and I'm just not awesome at math.

Answer 16

Ok, let's deduce the formula, suppose we have the element one of the sequency \(a_1\) and we what to find the second element of the sequency, then:
\(a_2 = a_1*q\), the third element will be \(a_3 = a_2 * q\), and so on...
For the n-th element: \(a_n = a_{n-1} * q = a_{n-2}*q^2 = ... = a_1*q^{n-1}\)

Answer 17

It's multiple choice on a timed test so honestly I'm just gonna guess at this point. Thanks for your help though.

Answer 18

q=1.00475
a1 = -8
a9=a1 q^8
a9=-8*(1.00475)^8
slve u will get answer

Answer 19

Thanks!

Answer 20

did u get the answer

Answer 21

Yeah, I did. It's -524,288 right?

Answer 22

whats the value of this (1.00475)^8 ???

Answer 23

I've already submitted the test so if it isn't right, then oh well.

Answer 24

just say whats the value of this (1.00475)^8 ???

Answer 25

1.0386377874

Answer 26

I got the right answer so it's all good.

Answer 27

after multiplying1.0386377874 with -8 the answer is ??

Answer 28

There's no point to this anymore, the final answer is -524,288. That's what I needed.

Answer 29

ok

Answer 30

Thanks for your help!

Answer 31

i didnt get the answer