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

1024, 512, 256, 128,...

So, a1 = 1024.

r = 512/1024 = 1/2

r = 256/512 = 1/2

r = 128/256 = 1/2

Hence, nth term is

an = a1 *r^(n-1)

an = 1024 *(1/2)^(n-1)

an = 1024 *[(1/2)^n / (1/2)]

an = 1024 *[2 *(1/2)^n]

an = 2048 *[1^n / 2^n]

an = 2048 *[1 / 2^n]

an = 2048 / 2^n ----------------answer.

Check,

a3 = 256 --------given

256 =? 2048 / (2^3)

256 =? 2048 / 8

256 =? 256

Yes, so, OK.