Question

Which exponential function can be used to show the geometric sequence 40, 160, 640, . . . ?(1 point)
an=40(120)^n−1
an=40+4(n−1)
an=4(40)^n−1
an=40(4^)n−1

Answer 1

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

1. The first term of the sequence is \( a_1 = 40 \).
2. To find the common ratio, divide the second term by the first term:
\[
r = \frac{160}{40} = 4
\]
3. You can also check the ratio between the third term and the second term:
\[
r = \frac{640}{160} = 4
\]

Since the first term is \( 40 \) and the common ratio is \( 4 \), we can express the \( n \)-th term of the geometric sequence using the formula:
\[
a_n = a_1 \cdot r^{n-1} = 40 \cdot 4^{n-1}
\]

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

From the options given, the correct choice is:
\[
\boxed{a_n = 40(4^{n-1})}
\]