Find the tenth term of the geometric sequence with a2=1/2 a5=4?

The step is 2.
a2=1/2
a3=1
a4=2
a5=4
a10 = a5 * 2^5 = 4*32 = 128

any term a(n) = a1 r^(n-1), where a1=1st term and r=geometric ratio

a2 = a1 r^(2-1) = a1 r ....(1)
a5 = a1 r(5-1) = a1 r⁴

a5/a2 = a1 r⁴/a1 r
4/ ½ = r³
8 = r³
r = 2

plug in (1) to get

½ = a1(2)
a1 = ¼

a10 = a1 r^(10-1) = ¼ (2)⁹ = 128

hint:
rule
a(n) =a1 (r)^(n-1)

find r hten find n(10)