My question is below and i must use a geometric sequence formula to answer it

Question

The time it takes for a half of a sample of radioactive isotope to decay is called the half-life. Iodine-131 has a half-life of 8 days. If a hospital receives a shipment of 200mg of iodine-131, how much iodine-131 would remain after 32 days?

Answer 1

common ratio = r = 1/2, half life = 8 years

A1 = 200

A2 = A1(r)^1 = 200(1/2) = 100 after 8 years

A3 = A1(r)^2 = 200(1/4 = 50 after 16 years

A4 =A1(r)^3 = 200(1/8) = 25 mg after 32 years

AN = A1(r)^N-1

geometric sequence: 200,100,50,25, ...

for N = 1,2,3,4, ...