Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -12 and 768, respectively

Answer 1

So now u know the geometric sequence formula?

Answer 2

Well it's

an= a(r) ^ n-1
Where a=1st term
R=ratio
N= number of terms

Answer 3

@nikato i get that but how do i do it if i dont have the first term

Answer 4

Ok, u want to solve though system of equations.
Did u plug everything it so u have to different equations?

Answer 5

im honestly so confused

Answer 6

Ok, so just follow along

Answer 7

Thank you so much~

Answer 8

Plug in the numbers into the geometric formula

768=ar^4

-12=ar^1

Ok with this?

Answer 9

Where did you get the ^4 from?

Answer 10

So in the geoetric formula it's n-1. Since its the 5th term, it's 5-1 or 4

Answer 11

oh okay okay

Answer 12

@nikato

Answer 13

So now I'm gonna divide both equations

Answer 14

768=ar^4
------------
-12=ar^1

Answer 15

divided them by eachother

Answer 16

Remember a/a=1 and ur just subtracting exponents when u divide
So this equals

-64=r^3
Can u find r?

Answer 17

And yes, I divided them by each other

Answer 18

no :/

Answer 19

So u want to cube root both sides. Which u can do on ur calculator

Answer 20

-4

Answer 21

Or u can factor 64 which is 4x4x4 but becuz it's negative it's -4x-4x-4

Answer 22

Ok. Yes. So our r=-4

Answer 23

how do we find a?

Answer 24

So now let's plug it back into one of the original equation. Lets use the second one
-12=ar^1
So
-12=a(-4)^1
-12=a(-4)
So now, can u find a?

Answer 25

i got -3/4

Answer 26

wait no

Answer 27

3

Answer 28

would it be an=3*-4^n-1

Answer 29

Yea, correct. Great job!

Answer 30

Thank you so much i actually get it now!

Answer 31

Ur welcome!