Question

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

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

Answer 1

To determine which exponential function represents the geometric sequence 40, 160, 640, ..., we first identify the common ratio of the sequence.

1. The first term \( a_1 = 40 \).
2. The second term \( a_2 = 160 \).
3. The third term \( a_3 = 640 \).

To find the common ratio \( r \):

\[
r = \frac{a_2}{a_1} = \frac{160}{40} = 4
\]

\[
r = \frac{a_3}{a_2} = \frac{640}{160} = 4
\]

The common ratio \( r \) is 4.

The general form of a geometric sequence can be expressed as:

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

Substituting the values:

- \( a_1 = 40 \)
- \( r = 4 \)

We get:

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

So the correct answer is:

**an=40(4)n−1**
\( a_n = 40(4)^{n-1} \)