Provide the pseudocode for a recursive algorithm Solve$\_$E to evaluate the series E :

$E(1)=3$

$E(2)=3$

$E(3)=3$

$E(4)=3$

$E(n)=3^{**}E(n-1)+4$ for $n>4$

Using a recursive algorithm, how many times function $E($at previous point$)$ is calculated to evaluate:

A$.E(6)$

B$.E(5)$

C$.E(4)$

Indicate the first $5$ values of the recurrence sequence W :

$W(1)=2$

$W(2)=3$

$W(n)=W(n-1)(n-2)$ for $n>2$

Provide the pseudocode for a recursive algorithm $W$ to evaluate the series W $($same as above$)$:

$W(1)=2$

$W(2)=3$

$W(n)=W(n-1)(n-2)$ for $n>2$

Using a recursive algorithm, how many times the function W is calculated $($at previous point$),$ to evaluate:

A$.W(5)$

B$.W(3)$

C$.W(2)$

A set $T$ of numbers is defined recursively by

$1\mathrm{.}2$ belongs to T $.$

If $x$ belongs to $T,$ so does $x+3$ and $2^{**}x.$

A$.$ Indicate $4$ elements of set T

B$.$ Does it $11$ belong to the set $T?$

C$.$ Does it $6$ belong to the set T $?$