Question

Select the response that creates an accurate formula for the sequence 2, 3.5, 6.125, 10.71875….
y = 2(1.75)^x
y = 2/1.5x
y = 2(1.5)^x
y =2 + 1.75x

Answer 1

To find the correct formula for the given sequence \(2, 3.5, 6.125, 10.71875,\) let's first analyze the terms more closely.

1. **Identifying the pattern:**
- The difference between the first two terms: \(3.5 - 2 = 1.5\)
- The difference between the second and third terms: \(6.125 - 3.5 = 2.625\)
- The difference between the third and fourth terms: \(10.71875 - 6.125 = 4.59375\)

The differences do not form a simple arithmetic sequence.

2. **Considering exponential or multiplicative growth:**
- Checking the ratios of consecutive terms:
- \(3.5 / 2 = 1.75\)
- \(6.125 / 3.5 = 1.75\)
- \(10.71875 / 6.125 \approx 1.75\)

This suggests the sequence could be modeled by an exponential function of the form:
\[
y = a \cdot (b)^x
\]

Where \(a\) is the initial term of the sequence and \(b\) is the common ratio.

3. **Finding \(a\) and \(b\):**
Since the first term \(y(0) = 2\), we have:
\[ a = 2 \]
Observing the ratio, we see \(b = 1.75\).

Thus, the formula for the sequence appears to take the form:
\[
y = 2(1.75)^x
\]

4. **Evaluating the Answer Choices:**
Among the provided options:
- **y = 2(1.75)^x** is a match.

This fits our findings.

Thus, the correct response that creates an accurate formula for the sequence is:
**y = 2(1.75)^x**.