Question

Consider the geometric sequence: 1, 3, 9, 27, …… If n is an integer, which of these functions generates the sequence?

a) f(x)=2 x
b) f(x)=3 x
c) f(x)=x 2
d) f(x)= 1/2x
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Answer 1

The function that generates the given geometric sequence is f(x) = 3^(x-1).

Step-by-step explanation:

The given sequence is a geometric sequence. In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor called the common ratio. In this case, the common ratio is 3, since each term is obtained by multiplying the previous term by 3.

So, the function that generates the sequence is f(x) = 3x-1. This function raises the common ratio to the power of (x-1), where x represents the position of the term in the sequence.

For example, when x = 1, the first term of the sequence is 31-1 = 30 = 1.