Geometric Sequences Quick Check

Question

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

an=40(120)n−1
a subscript n baseline equals 40 left parenthesis 120 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(4)n−1
a subscript n baseline equals 40 left parenthesis 4 right parenthesis superscript n minus 1 baseline

an=4(40)n−1

Answer 1

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

The first term \( a_1 \) is 40. To find the common ratio \( r \), we can divide the second term by the first term:

\[ r = \frac{160}{40} = 4 \]

Now, we can express the nth term \( a_n \) of a geometric sequence using the formula:

\[ a_n = a_1 \cdot r^{n-1} \]

Substituting \( a_1 = 40 \) and \( r = 4 \):

\[ a_n = 40 \cdot 4^{n-1} \]

Thus, the correct exponential function that represents the sequence is:

\[ \boxed{a_n = 40(4)^{n-1}} \]

This corresponds to the response:

an=40(4)n−1