Which function best models the geometric sequence 2, 4, 8, 16, 32, … ?
A. A(n) = 2n
B. A(n) = 2^n
C. A(n) = n^2
D. A(n) = n^2 + 1
I got B is that correct? Please correct me if I am wrong
B is good.
To determine the correct function that models a geometric sequence, we need to understand the characteristics of a geometric sequence. A geometric sequence is a sequence in which each term is found by multiplying the previous term by a constant value called the common ratio.
In the given sequence 2, 4, 8, 16, 32, ... , we can observe that each term is obtained by multiplying the previous term by 2. Hence, the common ratio is 2.
Let's check the given options:
A. A(n) = 2n
This option represents a linear function, as it multiplies the term number (n) by a constant value (2). It does not match the pattern of a geometric sequence where each term is obtained by multiplying the previous term by a constant ratio.
B. A(n) = 2^n
This option represents an exponential function, where each term is found by raising the base (2) to the power of the term number (n). This matches the pattern of a geometric sequence, where each term is obtained by multiplying the previous term by a constant ratio (2). Consequently, option B is the correct answer.
C. A(n) = n^2
This option represents a quadratic function. It does not match the pattern of a geometric sequence where each term is obtained by multiplying the previous term by a constant ratio.
D. A(n) = n^2 + 1
Similar to option C, this option represents a quadratic function and does not match the pattern of a geometric sequence.
So, your initial answer of option B is correct! The function A(n) = 2^n best models the given geometric sequence.