Question

Write an equation that models the sequence 400, 200, 100, 50, ...

A) y = 400(2x)
B) y = 50 (2x)
C) y =
1
2
x + 400
D) y = 400(
1
2
)x-1

Answer 1

D

Explanation:

The terms of the sequence

400, 200, 100, 50, ...

These are the terms of a geometric sequence with n th term

`a_(n)` = a
`(r)^(n-1)`

where a is the first term and r the common ratio

r =
`(200)/(400)` =
`(100)/(200)` =
`(1)/(2)`

The first term a = 400, hence

y = 400
`((1)/(2)) ^(x-1)` → D