Question

A geometric sequence begins with 72, 36, 18, 9, …

Which option below represents the formula for the sequence?

f(n) = 72(2)n−1
f(n) = 72(2)n+1
f(n) = 72(0.5)n−1
f(n) = 72(0.5)n+1

Answer 1

Answer:

f(n) = 72(0.5)^(n - 1)

Step-by-step explanation:

a_1 = 72 = 72 = 72 × 0.5^0

a_2 = 36 = 72 × 0.5^1

a_3 = 18 = 72 × 0.5 × 0.5 = 72 × 0.5²

a_4 = 9 = 72 × 0.5³

Notice that for each term, the exponent is 1 less than the term number.

a_n = 72(0.5)^(n - 1)

f(n) = 72(0.5)^(n - 1)