Final answer:
The explicit form of the given recursive sequence is a(n) = 4 × (3/4)^(n-1), which correctly represents the pattern that each term is 3/4 of the previous term, starting with the first term a₁ = 4.
Step-by-step explanation:
The explicit form of the sequence defined recursively by a₁ = 4 and aₙ = ¾ × aₙ₋₁ can be determined using the recursive relationship. To find the explicit form of a sequence, you observe the pattern that emerges from the recursive definition.
For the second term in the sequence, we have a₂ = ¾ × a₁ = ¾ × 4 = 3. For the third term, a₃ = ¾ × a₂ = (¾)^2 × 4. Continuing this pattern for the n-th term, we can see that each term involves the initial value of 4 multiplied by (¾) raised to the power of one less than the term number, which gives us a(n) = 4 × (¾)^(n-1).
Therefore, the correct explicit form of the sequence is Option A: a(n) = 4 × (¾)^(n-1).