We're analyzing each case to determine the solution.
we know that the sequence's formula is
[tex]f(n + 1) = 1.5f(n)[/tex]
case a)
we have the sequence
[tex]-12,-18,-27,...[/tex]
Let
[tex]f(1)=-12[/tex]
with the formula find the value of [tex]f(2)[/tex] and [tex]f(3)[/tex] and compare
Find the value of [tex]f(2)[/tex]
[tex]n=1[/tex]
[tex]f(1 + 1) = 1.5f(1)[/tex]
[tex]f(2) = 1.5*(-12)=-18[/tex]
Find the value of [tex]f(3)[/tex]
[tex]n=2[/tex]
[tex]f(2 + 1) = 1.5f(2)[/tex]
[tex]f(3) = 1.5*(-18)=-27[/tex]
therefore
The sequence case a) could be generated using the formula
case b)
we have the sequence
[tex]-20,30,-45,...[/tex]
Let
[tex]f(1)=-20[/tex]
with the formula find the value of [tex]f(2)[/tex] and [tex]f(3)[/tex] and compare
Find the value of [tex]f(2)[/tex]
[tex]n=1[/tex]
[tex]f(1 + 1) = 1.5f(1)[/tex]
[tex]f(2) = 1.5*(-20)=-30[/tex]
Find the value of [tex]f(3)[/tex]
[tex]n=2[/tex]
[tex]f(2 + 1) = 1.5f(2)[/tex]
[tex]f(3) = 1.5*(-30)=-45[/tex]
therefore
The sequence case b) could not be generated using the formula
case c)
we have the sequence
[tex]-18,-16.5,-15,...[/tex]
Let
[tex]f(1)=-18[/tex]
with the formula find the value of [tex]f(2)[/tex] and [tex]f(3)[/tex] and compare
Find the value of [tex]f(2)[/tex]
[tex]n=1[/tex]
[tex]f(1 + 1) = 1.5f(1)[/tex]
[tex]f(2) = 1.5*(-18)=-27[/tex]
Find the value of [tex]f(3)[/tex]
[tex]n=2[/tex]
[tex]f(2 + 1) = 1.5f(2)[/tex]
[tex]f(3) = 1.5*(-27)=-40.5[/tex]
therefore
The sequence case c) could not be generated using the formula
case d)
we have the sequence
[tex]-16,-17.5,-19,...[/tex]
Let
[tex]f(1)=-16[/tex]
with the formula find the value of [tex]f(2)[/tex] and [tex]f(3)[/tex] and compare
Find the value of [tex]f(2)[/tex]
[tex]n=1[/tex]
[tex]f(1 + 1) = 1.5f(1)[/tex]
[tex]f(2) = 1.5*(-16)=-24[/tex]
Find the value of [tex]f(3)[/tex]
[tex]n=2[/tex]
[tex]f(2 + 1) = 1.5f(2)[/tex]
[tex]f(3) = 1.5*(-24)=-36[/tex]
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
[tex]-12,-18,-27,...[/tex]
Answer:
Answer is A. –12, –18, –27, ...
Step-by-step explanation:
