Question

-2 2/3, -5 1/3, -10 2/3, -21 1/3, -42 2/3, ... Which formula can be use 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)

Answer 1

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

f(x+1)=2(-2 2/3)=-5 1/3
f(x+1)=2(-5 1/3)=-10 2/3
f(x+1)=2(-10 2/3)=-21 1/3
f(x+1)=2(-21 1/3)=-42 2/3

Answer 2

Option D is the correct answer.

Explanation:

`-2(2)/(3)=-(8)/(3)\\\\-5(1)/(3)=-(16)/(3)\\\\-10(2)/(3)=-(32)/(3)\\\\-21(1)/(3)=-(64)/(3)`

So the series is

`-(8)/(3),-(16)/(3),-(32)/(3),-(64)/(3).............`

`(-(16)/(3))/(-(8)/(3))=2\\\\(-(32)/(3))/(-(16)/(3))=2\\\\(-(64)/(3))/(-(32)/(3))=2`

We can see that each term is twice of the previous term

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

Option D is the correct answer.