To find a formula for the sequence 2, 3.5, 6.125, 10.71875, we need to analyze the pattern in the sequence and determine the correct formula among the given options.
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Starting from the first term (2):
- 2 to 3.5: This is an increase of 1.5.
- 3.5 to 6.125: This is an increase of 2.625.
- 6.125 to 10.71875: This is an increase of 4.59375.
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The differences between these terms don't appear to follow a simple linear or polynomial pattern, suggesting that the sequence could be exponential or follow some multiplicative process.
When we look closely, the sequence seems to resemble the form of: \[ y = a \cdot b^x + c \] However, the question provides specific formulas to choose from.
After inspecting the options:
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y = 2 + 1.75x - This looks linear and doesn't fit the exponential growth.
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y = 2(1.75)x − 1 - This one has a coefficient, but the input seems incorrect for a sequence as it is unclear how x relates to the terms or if the exponent is coherent.
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y = 21.5x - This is also more complicated than needed and doesn't seem to match the outputs.
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y = 2(1.5)x - This appears more linear, but with no exponential growth.
What seems to best fit an exponential growth pattern, without performing the full calculations to find an exact algebraic relationship based on the given choices, is likely the 2nd option:
y = 2(1.75)^(x-1)
It indicates a sequence growth that starts at 2 and multiplies by a factor of 1.75 for each increment in x.
Thus, the response that creates an accurate formula for the sequence is:
y = 2(1.75)^(x - 1).