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

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)

Sasha doubled the swiming time /week

Mona increased the swiming time by 10 min every week

So Sasha's method is exponetial while Mona's method is linear