Question

Which function forms a geometric sequence when x = 1, 2, 3, ...?

1) f(x) = 8x - 9
2) f(x) = -2(3/4)ˣ
3) f(x) = (2/3)x⁵
4) f(x) = 6 - (4/x)

Answer 1

The function that forms a geometric sequence when x = 1, 2, 3, ... is f(x) = -2(3/4)ˣ.

Step-by-step explanation:

The function that forms a geometric sequence when x = 1, 2, 3, ... is f(x) = -2(3/4)ˣ.

To determine if a function forms a geometric sequence, we need to check if the ratio of any two consecutive terms is constant.

For option 2, when x = 1, we have f(1) = -2(3/4)¹ = -2(3/4) = -6/4 = -1.5. When x = 2, we have f(2) = -2(3/4)² = -2(9/16) = -18/16 = -1.125. The ratio between these terms is -1.125/-1.5 = 3/4. Therefore, option 2 forms a geometric sequence.