Which exponential function can be used to show the geometric sequence 40, 160, 640, . . . ?(1 point)

Question

Responses

an=40(4)n−1
a subscript n baseline equals 40 left parenthesis 4 right parenthesis superscript n minus 1 baseline

an=4(40)n−1
a subscript n baseline equals 4 left parenthesis 40 right parenthesis superscript n minus 1 baseline

an=40+4(n−1)
a subscript n baseline equals 40 plus 4 left parenthesis n minus 1 right parenthesis

an=40(120)n−1

Answer 1

To find the exponential function that represents the given geometric sequence 40, 160, 640, ..., we first identify the first term and the common ratio.

1. The first term \( a_1 \) is 40.
2. To find the common ratio \( r \), we can divide the second term by the first term:
   \( r = \frac{160}{40} = 4 \).
   We can verify this by dividing the third term by the second term:
   \( r = \frac{640}{160} = 4 \).

Since this is a geometric sequence, the general formula for the n-th term can be written as: \[ a_n = a_1 \cdot r^{n-1} \]

Substituting the values for \( a_1 \) and \( r \): \[ a_n = 40 \cdot 4^{n-1} \]

Thus, the exponential function that describes the geometric sequence is: \[ a_n = 40(4)^{n-1} \]

So, the correct response is: a_n = 40(4)^{n-1}