Select the response that creates an accurate formula for the sequence 2, 3.5, 6.125. 10.71875 . . .

Question

.(1 point)
Responses

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

y=21.5x
y equals Start Fraction 2 over 1.5 x End Fraction

y=2+1.75x
y equals 2 plus 1.75 x

y=2(1.5)x

Answer 1

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

The sequence seems to involve multiplying by an increasing factor.

1. From \(2\) to \(3.5\): \(\frac{3.5}{2} = 1.75\)
2. From \(3.5\) to \(6.125\): \(\frac{6.125}{3.5} \approx 1.75\)
3. From \(6.125\) to \(10.71875\): \(\frac{10.71875}{6.125} \approx 1.75\)

It appears that each term is being multiplied by approximately \(1.75\).

Now, looking at the response options:

• y=2(1.75)x−1: This does suggest that the sequence starts with 2 and each term is multiplied by \(1.75\) raised to the power of \(x-1\).

Overall, the correct formula that accurately represents the sequence based on the multiplication by \(1.75\) would be:

y=2(1.75)x−1