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

y=2(1.75)x−1
y equals 2 left parenthesis 1.75 right parenthesis superscript x baseline

y=21.5x

Answer 1

To find an accurate formula for the given sequence \(2, 3.5, 6.125, 10.71875\), we can analyze the pattern of the numbers to derive a formula.

1. First, calculate the ratio between consecutive terms:
- \( \frac{3.5}{2} = 1.75 \)
- \( \frac{6.125}{3.5} \approx 1.75 \)
- \( \frac{10.71875}{6.125} \approx 1.75 \)

The ratio between consecutive terms appears to be consistent, indicating that the sequence may be exponential.

2. The first term is \(a_1 = 2\), and each term can be approximated by the formula \(y = 2(1.75)^{x-1}\), where \(x\) corresponds to the position of the term in the sequence.

Among the given options, the response that fits this pattern is:

**y = 2(1.75)^(x−1)**

This corresponds to the third option:

**y=2(1.75)x−1 y equals 2 left parenthesis 1.75 right parenthesis superscript x baseline**

This should accurately generate the terms of the sequence.