Question

Select the response that creates an accurate formula for the sequence 2, 3.5, 6.125. 10.71875 . . ..(1 point)
Responses

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

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

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

y=2(1.75)^x

Answer 1

To find the accurate formula for the given sequence \(2, 3.5, 6.125, 10.71875, \ldots\), let's analyze the numbers:

1. The sequence appears to have a base number starting from \(2\).
2. When we look at how the terms progress:

- \(2 \rightarrow 3.5\) (which is \(2 + 1.5\))
- \(3.5 \rightarrow 6.125\) (which is \(3.5 + 2.625\))
- \(6.125 \rightarrow 10.71875\) (which is \(6.125 + 4.59375\))

It seems like the increments (differences) are not consistent, indicating a multiplicative relationship.

Calculating the ratios:

- \( \frac{3.5}{2} = 1.75 \)
- \( \frac{6.125}{3.5} = 1.75 \)
- \( \frac{10.71875}{6.125} \approx 1.75 \)

From this analysis, it looks like the sequence could be modeled by a formula involving multiplication by a factor of \(1.75\).

The candidate that matches the pattern of starting with \(2\) and multiplying by \(1.75\) is:

**y = 2(1.75)^x**

So the correct response is:

**y = 2(1.75)^x**