Final answer:
The correct recursive formula for the geometric sequence 1/2, 3/4, 9/8, 27/16 is option C) a1 = 1/2; an = an-1 × (3/2) for n≥2.
Step-by-step explanation:
A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio. The next term of the sequence is produced when we multiply a constant (which is non-zero) to the preceding term. The geometric sequence given is 1/2, 3/4, 9/8, 27/16. To determine the recursive formula for this sequence, we need to find a relationship between successive terms. Observing the sequence, each term is obtained by multiplying the previous term by 3/2. Therefore, the correct recursive formula is C) a1 = 1/2; an = an-1 × (3/2) for n≥2. The first term a1 is given as 1/2, and for each term an, we multiply the previous term an-1 by 3/2 to get the next term.