To determine which response creates an accurate formula for the sequence \(2, 3.5, 6.125, 10.71875, \ldots\), let's analyze the pattern in the sequence:
- Calculate the ratios between consecutive terms:
- \( \frac{3.5}{2} = 1.75 \)
- \( \frac{6.125}{3.5} \approx 1.75 \)
- \( \frac{10.71875}{6.125} \approx 1.75 \)
This suggests that the sequence might be related to a geometric progression where each term is multiplied by approximately \( 1.75 \).
- Identifying the formula: If the sequence begins at \(2\) and each subsequent term is multiplied by \(1.75\), a suitable formula would resemble: \[ y = 2(1.75)^{x-1} \] where \( x \) starts at \(1\) for the first term \(y(1) = 2\).
Let's check if any of the given responses match this or represent the same logic:
- \(y = 2(1.5)^x\): This does not match, as the multiplication factor is wrong.
- \(y = \frac{2}{1.5^x}\): This also does not fit the pattern.
- \(y = 2 + 1.75x\): This is a linear formula, not matching the exponential nature of the sequence.
- \(y = 2(1.75)^{x-1}\): This correctly reflects the pattern identified.
Thus, the response that creates an accurate formula for the sequence is: \(y = 2(1.75)^{x-1}\).
(Note: If this specific option was not listed, please ensure to check the formatting of the answers as there might be a representation issue).
1 answer