What exponential function can be used to show the geometric sequence 40, 160, 640, . . . ?

A. A n = 40 + 4 (n - 1)
B. A n = 4(40)^n - 1
C. A n = 40(120)^n - 1
D. A n = 40(4)^n - 1

1 answer

The common ratio for this geometric sequence is 4 (each term is obtained by multiplying the previous term by 4).

To find the exponential function that represents this sequence, we can use the form A_n = A * r^(n-1), where A is the first term and r is the common ratio.

In this case, A = 40 and r = 4.

Therefore, the correct exponential function for the given geometric sequence is D. A_n = 40 * (4)^(n-1).