Question

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

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

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

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

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

Answer 1

To find an accurate formula for the sequence 2, 3.5, 6.125, 10.71875, we can explore the growth pattern of the sequence:

1. **Calculating Ratios**:
- The first term \(a_1 = 2\).
- The second term \(a_2 = 3.5\) which is \((2 * 1.75)\).
- The third term \(a_3 = 6.125\) which is \((3.5 * 1.75)\).
- The fourth term \(a_4 = 10.71875\) which is \((6.125 * 1.75)\).

From the above, it appears the sequence is being multiplied by \(1.75\) each time after the first term.

2. **General Formula**: Based on the pattern, it looks like the sequence could be expressed as:
\[
y = 2(1.75)^{x-1}
\]
Here, the term \(x\) represents the position in the sequence (where \(x=1\) gives the first term, \(x=2\) gives the second term, etc.)

However, from the given responses, the closest match that retains the structure we derived (using \(1.75\)) is:

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

So, given the options:

- **y = 2(1.75)^x** (this would yield exact matches as explained)

Thus, the correct response from the provided options is:

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