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

u know n-th term of a geometri series is
tn=ar^(n-1)

Answer 2

so second tetm t2=ar^(2-1)=-12
ar=-12

Answer 3

now 5 th term is t5=ar^(5-1)=ar^4=768

Answer 4

now devide those two equation

Answer 5

-64

Answer 6

yes

Answer 7

r=?

Answer 8

is -64?

Answer 9

r^3=-64
r=-4

Answer 10

again
ar=-12
a(-4)=-12
a=?

Answer 11

a=3

Answer 12

now nth term is
tn=ar^(n-1)=?

Answer 13

What I don't quite understand is why divide the two equations to get -64 and they how we get r=-4?