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?

Answer 1

Answer:

Option D is the correct answer.

Step-by-step explanation:

$-2\frac{2}{3}=-\frac{8}{3}\\\\-5\frac{1}{3}=-\frac{16}{3}\\\\-10\frac{2}{3}=-\frac{32}{3}\\\\-21\frac{1}{3}=-\frac{64}{3}$

So the series is

       $-\frac{8}{3},-\frac{16}{3},-\frac{32}{3},-\frac{64}{3}.............$

     $\frac{-\frac{16}{3}}{-\frac{8}{3}}=2\\\\\frac{-\frac{32}{3}}{-\frac{16}{3}}=2\\\\\frac{-\frac{64}{3}}{-\frac{32}{3}}=2$

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

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

Option D is the correct answer.

Answer 2

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