Question

Which function can be used to represent the graphed geometric sequence?

f(x) = 80(One-fourth) Superscript x minus 1
f(x) = 320(One-fourth) Superscript x minus 1
f(x) = 80(4)x – 1
f(x) = 320(4)x – 1

Answer 1

f(x) = 80
`((1)/(4)) ^(x-1)`

Explanation:

the nth term of a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

given the points (1, 80 ) , (2, 20 ) , (3, 5 )

then

x | 1 2 3

y | 80 20 5

with a₁ = 80 and r =
`(a_(2) )/(a_(1) )` =
`(20)/(80)` =
`(1)/(4)` , then

f(x) = 80
`((1)/(4)) ^(x-1)`

Answer 2

A) 80(One-fourth) Superscript x minus 1

Explanation:

Used the table function on my calculator. 1/4 of 80 is 20 and 1/4 of 20 is 5. f(1) = 80 f(2) = 20 f(3) = 5 and so on. Hope that made sense!