Final answer:
The equation representing a geometric sequence out of the given options is (d) y = 4^x + 3, because it involves the terms being multiplied by a common ratio when x is an integer, which is a characteristic of a geometric sequence.
Step-by-step explanation:
The question asks which equation represents a geometric sequence. A geometric sequence follows the form an = a1 · r(n-1), where an is the nth term of the sequence, a1 is the first term, and r is the common ratio between the terms. Looking at the options provided:
- (a) y = 2x + 3 is a linear equation, not geometric.
- (b) y = x^2 + 5x - 6 is a quadratic equation, not geometric.
- (c) y = x^3 - 1 is a polynomial of degree 3, not geometric.
- (d) y = 4^x + 3 represents an exponential function, which is similar to a geometric sequence when x is restricted to the integers, as the term 4^x implies the multiplication of a common ratio (4) to successive powers.
Therefore, the equation that represents a geometric sequence is (d) y = 4^x + 3.