Question

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

3.5
,

6.125.

10.71875

.

.

.
.(1 point)
Responses

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

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

y=2+1.75x
𝑦
=
2
+
1.75
𝑥
y equals 2 plus 1.75 x

y=2(1.75)x−1

Answer 1

To determine which response creates an accurate formula for the sequence \(2, 3.5, 6.125, 10.71875, \ldots\), let's analyze the pattern in the sequence:

1. **Calculate the ratios between consecutive terms:**
- \( \frac{3.5}{2} = 1.75 \)
- \( \frac{6.125}{3.5} \approx 1.75 \)
- \( \frac{10.71875}{6.125} \approx 1.75 \)

This suggests that the sequence might be related to a geometric progression where each term is multiplied by approximately \( 1.75 \).

2. **Identifying the formula:**
If the sequence begins at \(2\) and each subsequent term is multiplied by \(1.75\), a suitable formula would resemble:
\[
y = 2(1.75)^{x-1}
\]
where \( x \) starts at \(1\) for the first term \(y(1) = 2\).

Let's check if any of the given responses match this or represent the same logic:

- \(y = 2(1.5)^x\): This does not match, as the multiplication factor is wrong.
- \(y = \frac{2}{1.5^x}\): This also does not fit the pattern.
- \(y = 2 + 1.75x\): This is a linear formula, not matching the exponential nature of the sequence.
- **\(y = 2(1.75)^{x-1}\)**: This correctly reflects the pattern identified.

Thus, the response that creates an accurate formula for the sequence is:
**\(y = 2(1.75)^{x-1}\)**.

(Note: If this specific option was not listed, please ensure to check the formatting of the answers as there might be a representation issue).