Final answer:
The common ratio of the geometric sequence with the given 2nd and 5th terms is ¾.
Step-by-step explanation:
The question is asking to find the common ratio of a geometric sequence given the 2nd and 5th terms. The 2nd term is ½ and the 5th term is ⅓27/128. To find the common ratio (r), we use the formula for the nth term of a geometric sequence, which is ar(n-1), where 'a' is the first term and 'n' is the term number.
Since the 5th term is equal to the 2nd term multiplied by the common ratio cubed (because 5 - 2 = 3), we can set up an equation: (½) × r3 = ⅓27/128. Solving for 'r' gives us:
r3 = (⅓27/128)/(½) = ⅓27/(128 × 2) = ⅓27/256. When we take the cube root of both sides, we find that r = ⅓3/4.