Question

A sequence is defined by the recursive formula f(n + 1) = 1.5f(n). Which sequence could be generated using the formula?

–12, –18, –27, ...

–20, 30, –45, ...

–18, –16.5, –15, ...

–16, –17.5, –19, ...

Answer 1

Answer is A. –12, –18, –27, ...

Explanation:

Answer 2

We're analyzing each case to determine the solution.

we know that the sequence's formula is

`f(n + 1) = 1.5f(n)`

case a)

we have the sequence

`-12,-18,-27,...`

Let

`f(1)=-12`

with the formula find the value of
`f(2)` and
`f(3)` and compare

Find the value of
`f(2)`

`n=1`

`f(1 + 1) = 1.5f(1)`

`f(2) = 1.5*(-12)=-18`

Find the value of
`f(3)`

`n=2`

`f(2 + 1) = 1.5f(2)`

`f(3) = 1.5*(-18)=-27`

therefore

The sequence case a) could be generated using the formula

case b)

we have the sequence

`-20,30,-45,...`

Let

`f(1)=-20`

with the formula find the value of
`f(2)` and
`f(3)` and compare

Find the value of
`f(2)`

`n=1`

`f(1 + 1) = 1.5f(1)`

`f(2) = 1.5*(-20)=-30`

Find the value of
`f(3)`

`n=2`

`f(2 + 1) = 1.5f(2)`

`f(3) = 1.5*(-30)=-45`

therefore

The sequence case b) could not be generated using the formula

case c)

we have the sequence

`-18,-16.5,-15,...`

Let

`f(1)=-18`

with the formula find the value of
`f(2)` and
`f(3)` and compare

Find the value of
`f(2)`

`n=1`

`f(1 + 1) = 1.5f(1)`

`f(2) = 1.5*(-18)=-27`

Find the value of
`f(3)`

`n=2`

`f(2 + 1) = 1.5f(2)`

`f(3) = 1.5*(-27)=-40.5`

therefore

The sequence case c) could not be generated using the formula

case d)

we have the sequence

`-16,-17.5,-19,...`

Let

`f(1)=-16`

with the formula find the value of
`f(2)` and
`f(3)` and compare

Find the value of
`f(2)`

`n=1`

`f(1 + 1) = 1.5f(1)`

`f(2) = 1.5*(-16)=-24`

Find the value of
`f(3)`

`n=2`

`f(2 + 1) = 1.5f(2)`

`f(3) = 1.5*(-24)=-36`

therefore

The sequence case d) could not be generated using the formula

therefore

the answer is

The sequence case a) could be generated using the formula

`-12,-18,-27,...`