Question

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

Answer 1

Answer:

Answer is A. –12, –18, –27, ...

Step-by-step 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

$-12,-18,-27,...$