Question

Which formula can be used to describe the sequence? f(x + 1) = –2f(x) f(x + 1) = -1/2 f(x) f(x + 1) = 1/2f(x) f(x + 1) = 2f(x)

Answer 1

The complete question is
-2 2/3, -5 1/3, -10 2/3, -21 1/3, -42 2/3, ... Which formula can be used to describe the sequence?

a. f(x + 1) = –2f(x)
b. f(x + 1) = f(x)
c. f(x + 1) = -f(x)
d. f(x + 1) = 2f(x)

case a) f(x + 1) = –2f(x)
for f(x)=-2 2/3
f(x+1)=-2*[-2 2/3]=5 1/3
5 1/3 is not -5 1/3
therefore
this is not the formula

case b) f(x + 1) = f(x)
for f(x)=-2 2/3
f(x+1)=-2 2/3
-2 2/3 is not -5 1/3
therefore
this is not the formula

case c) f(x + 1) = -f(x)
for f(x)=-2 2/3
f(x+1)=2 2/3
2 2/3 is not -5 1/3
therefore
this is not the formula

case d) f(x + 1) =2f(x)
for f(x)=-2 2/3
f(x+1)=2*[-2 2/3]=-5 1/3

for f(x)=-5 1/3
f(x+1)=2*[-5 1/3]=-10 2/3

for f(x)=-10 2/3
f(x+1)=2*[-10 2/3]=-21 1/3

for f(x)=-21 1/3
f(x+1)=2*[-21 1/3]=-42 2/3

therefore 
the answer is the option
d. f(x + 1) = 2f(x)

Answer 2

Answer:

f(x + 1) = 2f(x)

Step-by-step explanation:

In the figure attached, the complete question is shown. Taking as x the first point, f(x)=-2 2/3, for the next point, x+1, f(x+1) = -5 1/3 = 2*(-2 2/3)  = 2f(x); taking as x the second point, f(x)=-5 1/3, for the next point, x+1, f(x+1) = -10 2/3 = 2*(-5 1/3)  = 2f(x); and so on.