Question

Select the response that creates an accurate formula for the sequence
2, 3.5, 6.125. 10.71875 . . . . (1 point)
y = 2 + 1.75x
y =
2
1.5x
y = 2(1.5)
x
y = 2(1.75)
x − 1

Answer 1

To determine which formula accurately represents the sequence \(2, 3.5, 6.125, 10.71875, \ldots\), let's analyze the given options and the pattern in the sequence.

Let's evaluate the provided terms:

1. \(2\) (first term)
2. \(3.5\) (second term)
3. \(6.125\) (third term)
4. \(10.71875\) (fourth term)

Calculating the differences between the terms:

- From \(2\) to \(3.5\), the difference is \(1.5\).
- From \(3.5\) to \(6.125\), the difference is approximately \(2.625\).
- From \(6.125\) to \(10.71875\), the difference is approximately \(4.59375\).

The differences appear to be increasing, but let's check for a pattern more closely related to the specific options.

Now let’s look at each of the provided options:

1. **\(y = 2 + 1.75x\)**: This is a linear equation and would not fit the provided terms which appear to increase non-linearly.

2. **\(y = 2(1.5)^x\)**: This suggests an exponential growth starting with 2, which might fit. We can check values:
- For \(x = 0\): \(y = 2(1.5)^0 = 2\) (matches first term)
- For \(x = 1\): \(y = 2(1.5)^1 = 3\) (should match second term, does not)

3. **\(y = 2(1.75)^x\)**: Another form of exponential growth:
- For \(x = 0\): \(y = 2(1.75)^0 = 2\) (matches first term)
- For \(x = 1\): \(y = 2(1.75)^1 = 3.5\) (matches second term)
- For \(x = 2\): \(y = 2(1.75)^2 = 6.125\) (matches third term)
- For \(x = 3\): \(y = 2(1.75)^3 = 10.71875\) (matches fourth term)

4. **\(y = 2(1.75)^{x - 1}\)**: This would imply a shift in the index:
- For \(x = 1\): \(y = 2(1.75)^{1 - 1} = 2\) (does not match the first term)

Given the evaluations, the correct response that creates an accurate formula for the sequence is:

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