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

Question

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.