What is a formula for the nth term of the given sequence?

36, 12, 4 ...

A. a n = 108 (3) ^n-1

B. a n = 36 (3) ^-n

C. a n = 108 (1/3) ^-n

D. a n = 36 (3) ^1-n

Answer: option D is the correct answer.

Step-by-step explanation:

The given sequence is a geometric sequence because the consecutive terms differ by a common ratio.

The formula for determining the nth term of a geometric progression is expressed as

an = a1r^ (n - 1)

Where

a1 represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a1 = 36

r = 12/36 = 4/12 = 1/3

Therefore, the formula for the nth term of the sequence is

an = 36 * 1/3^ (n - 1)

an = 36 * 3^-1 (n - 1)

an = 36 * 3^ (-n + 1)

an = 36 * 3^ (1 - n)