Geometry sequences: How do I find the nth term

1. Find the 7th term and identify the equation for it: 3, 36, 432
(I just need to double check my work)

2. Find the 3rd term and identify the equation for it:
A1 = 16 and A4 = (27/4)
*I don't get this one at all...

For a geometric sequence, each term is multiplied by r, the common ratio, to get the next term.

an= a1(r)^(n-1)

1) a1= 3; You can find r by dividing : a2/a1= 36/3= 12

an= 3(12)^(n-1)

a7= 3(12)^6

2) a1= 16; a4= 27/4; to get a4, you would have to multiply by r, 3 times.

27/4= 16(r)^3; multiply by 1/16

27/64= r^3; find the cube root

3/4= r

Then an= 16(3/4)^(n-1)

Then a3= 16(3/4)^2= 16(9/16)= 9

Hoping this helps!