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

Question

.(1 point)
Responses

y=21.5x

y equals Start Fraction 2 over 1.5 x End Fraction
y=2(1.5)x
y equals 2 left parenthesis 1.5 right parenthesis superscript x baseline
y=2+1.75x
y equals 2 plus 1.75 x
y=2(1.75)x−1

Answer 1

To find the correct formula for the sequence 2, 3.5, 6.125, 10.71875, we can analyze how the sequence progresses.

1. Finding the ratios between terms:
   • The ratio of the second term to the first term: \( \frac{3.5}{2} = 1.75 \)
   • The ratio of the third term to the second term: \( \frac{6.125}{3.5} = 1.75 \)
   • The ratio of the fourth term to the third term: \( \frac{10.71875}{6.125} = 1.75 \)

This suggests that each term is multiplied by 1.75 to get the next term.

2. Formulating the equation based on the pattern: The general formula for a geometric sequence can be expressed as: \[ y = a \cdot r^{(x-1)} \] where \( a \) is the first term and \( r \) is the common ratio.

   Here, \( a = 2 \) (the first term) and \( r = 1.75 \). Therefore, we can write the formula as: \[ y = 2 \cdot (1.75)^{(x-1)} \]

3. Identifying the correct response: The response that aligns with our derived formula is: \[ y = 2(1.75)^{x-1} \]

Thus, the correct response is: \( y = 2(1.75)^{x-1} \)