Question

Find the 9th term of the geometric sequence.
3/4, -3/8, 3/16, -3/32, 3/64

Answer 1

okay back to the basics yeah?

what number do we keep multiplying to get the next?

Answer 2

\[a _{n} = a \times r ^{n - 1}\]

Answer 3

I don't know. There are negatives. @robz8

Answer 4

where are is the common ration and a is the first term.

Answer 5

@Emilyh117 okay let's just look at the first couple numbers...

how do we get from 3/4 to -3/8?

how about -3/8 to 3/16?

Answer 6

-1/8? @robz8

Answer 7

hmmmm nooooooo... not quite...

does 3/4 * (-1/8) == (3/8)?

i don't think it does..

try another number for your denominator

Answer 8

um. 2? @robz8

Answer 9

yes, 2 is in the denominator!

so using the formula that @some_someone gave us, where A is 3/4 and R is -1/2... plug in 9 for N

and BAM.. you got your 9th term!

Answer 10

I got 0.002929..... ? @robz8

Answer 11

okay, try not to use your calculator when you're doing this... :P @Emilyh117

Answer 12

Haha Okay... I got 3/6 for the fraction part

Answer 13

@robz8

Answer 14

@Emilyh117 where did you get 3/6 from?

plugging in A, R, and N, you should get (3/4)*(-1/2)^(9-1)

Answer 15

Oh. I got -3/8 @robz8

Answer 16

-3/8 is the second term. the question asks you to find the 9th term @Emilyh117

Answer 17

Oh my gosh.. So confusing. @robz8

Answer 18

haha calm down, you can do this... @Emilyh117

Answer 19

your first term is 3/4 ...... A

the number you multiply each time is -1/2... R

the term you want to find is 9.... N

the formula to find the Nth term is

A*R^(N-1)

Answer 20

Okay. -3/64?

Answer 21

@robz8

Answer 22

hmmm thats not exactly what i got... @Emilyh117

Answer 23

plugging it all in you should get

(3/4)*(-1/2)^8

Answer 24

Okay. I got that @robz8

Answer 25

@Emilyh117 okay... so what should your answer be then?

Answer 26

Alright so.. before I do the power, I got -3/8 @robz8

Answer 27

remember your order of operations!!! you must do the power first!

Answer 28

What!? So i would set -1/2^8? @robz8

Answer 29

you must do (-1/2)^8

and THEN multiply that by (3/4) @Emilyh117

Answer 30

OKay

Answer 31

so... what should you get for (-1/2)^8 ??? @Emilyh117

Answer 32

-1/256

Answer 33

not quite..... the power is 8 which is even, meaning that it will be a positive number, not negative

you should end up with 1/256 @Emilyh117

Answer 34

Oh. That's what I meant

Answer 35

now just mulitply that by 3/4 and you're good to go! :) @Emilyh117

Answer 36

I got 3/1024

Answer 37

there ya go!

see? that wasn't that bad, was it?! @Emilyh117

Answer 38

Hahah no. Sorry. I bet that was a nightmare for you.

Answer 39

well i've had a lot more practice for you. it's hard when you're doing things for the first time! @Emilyh117

Answer 40

Haha. It is. Thank you so much! @robz8

Answer 41

you're very welcome. Now on the next problem you have to do. Just break it down into steps. See what the difference between the numbers is to start @Emilyh117

Answer 42

Okay. Thanks

Answer 43

@Emilyh117 post again if you are having trouble

Answer 44

I will.