Select the response that creates an accurate formula for the sequence 2, 3.5, 6.125. 10.71875 . . .

Question

.(1 point)
Responses

y=2(1.5)x
y equals 2 left parenthesis 1.5 right parenthesis superscript x baseline

y=2(1.75)x−1
y equals 2 left parenthesis 1.75 right parenthesis superscript x baseline

y=21.5x
y equals Start Fraction 2 over 1.5 x End Fraction

y=2+1.75x

Answer 1

To find an accurate formula for the given sequence \(2, 3.5, 6.125, 10.71875\), we can analyze the terms to see if we can identify a pattern.

1. The first term is \(2\).
2. The second term is \(3.5\), which is \(2 \times 1.75\).
3. The third term is \(6.125\), which can be computed as \(3.5 \times 1.75\).
4. The fourth term is \(10.71875\), computed as \(6.125 \times 1.75\).

This suggests that each term is obtained by multiplying the previous term by \(1.75\). This indicates that the sequence can be expressed in the form of an exponentiation pattern.

Thus, the nth term can be represented as:

\[ y = 2 \times (1.75)^{(n-1)} \]

Looking at the options provided:

• \(y = 2(1.75)^{x-1}\) matches this form.

Therefore, the correct response is:

y = 2(1.75)^{x-1}