Consider the sequence

$$

$=$

$($

$$

$$

$)$

s$=($s

n

$$

$)$ defined by

$$

$$

$=$

$$

$$

$2$

$$

$$

$3$

$$

$2$

$+$

$3$

$$

$+$

$2$

$.$

s

n

$$

$=\backslash$pi $2$

n

$$

n

$2$

$+3$n$+2$

$3$

$$

$.$

Which of the following sequences

$$

$=$

$($

$$

$$

$)$

r$=($r

n

$$

$)$ satisfies

$\backslash$Delta

$$

$=$

$$

$\backslash$Delta r$=$s$?$

Hint: it helps to use the following:

your answer to Question $1,$

the fact that the sequence

$($

$2$

$$

$)$

$(2$

n

$)$ forward$-$differentiates to itself, and

the fact that

$\backslash$Delta

$\backslash$Delta is a linear operator $($just like the derivative$),$ so you know how it behaves with sums and multiples of sequences.