Final answer:
The sum of the first 12 terms of the given geometric sequence, rounded to the nearest whole number, is approximately 13981.
Step-by-step explanation:
The student is asking for the sum of the first 12 terms (s12) of a geometric sequence. To find the sum, we need to identify the first term (a1) and the common ratio (r) of the sequence. Given the sequence 16, 24, 36, 54, ..., we can see that a1 = 16 and by dividing each term by its preceding term, the common ratio r is 1.5. The formula for the sum of the first n terms of a geometric sequence is sn = a1(1 - rn)/(1 - r), when r ≠ 1.
Plugging the values into the formula, we get s12 = 16(1 - 1.512)/(1 - 1.5). Calculating this value, and rounding to the nearest whole number, gives us 13981. Therefore, the sum of the first 12 terms is approximately 13981, which is Option O in the choices provided by the student.