Question

The formula for the sum s of the first n terms in a geometric sequence is given by s = a * (1 - rⁿ) / (1 - r), where a is the initial value and r is the common ratio. A drug is prescribed for a patient to take 225 mg every 12 hours for 10 days. After 12 hours, about how much of the drug will remain in the patient's system?

1) 150 mg
2) 175 mg
3) 200 mg
4) 225 mg

Answer 1

In this case, 225 mg of the drug will remain in the patient's system after 12 hours

The answer is option ⇒4) 225 mg

Step-by-step explanation:

To find out how much of the drug will remain in the patient's system after 12 hours, we can use the formula for the sum of the first n terms in a geometric sequence.

The formula is: s = a * (1 - rⁿ) / (1 - r), where a is the initial value and r is the common ratio.

In this case, the initial value is 225 mg, the common ratio is 1/2 (since the patient takes 225 mg every 12 hours), and the number of terms is 1 (since we want to find the amount remaining after 1 term).

Plugging in the values, we get:

s = 225 * (1 - (1/2)¹) / (1 - (1/2))

simplifying the equation gives:

s = 225 * (1 - 1/2) / (1/2)

s = 225 * (1/2) / (1/2)

s = 225

The answer is option ⇒4) 225 mg