Question

What formula can be used to describe the sequence ?

Answer 1

I think this is the 3 one... can i have brainliest?

Answer 2

Answer:

The  formula which can be used to describe the sequence is:

                $f(x+1)=2f(x)$

Step-by-step explanation:

The sequence is given by:

         $-2\dfrac{2}{3},-5\dfrac{1}{3},-10\dfrac{2}{3},-21\dfrac{1}{3},-42\dfrac{2}{3},.....$

The terms of the sequence could also be written as:

$\dfrac{-8}{3},\dfrac{-16}{3},\dfrac{-32}{3},\dfrac{-64}{3},\dfrac{-128}{3},....$

This means that the first term of the sequence is:

$f(1)=\dfrac{-8}{3}$

The second term of the sequence is:

$f(2)=\dfrac{-16}{3}\\\\i.e.\\\\f(2)=2\times \dfrac{-8}{3}\\\\i.e.\\\\f(2)=2f(1)$

$f(3)=\dfrac{-32}{3}\\\\i.e.\\\\f(3)=2\times \dfrac{-16}{3}\\\\i.e.\\\\f(3)=2f(2)$

and so on.

                 Hence, the formula is given by:

           $f(x+1)=2f(x)$