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.
- 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.
- 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.