Q$1)$ Consider following algorithm

function$($A$[1..$n$])$

$\{$

if $n=1$ then return;

for $i$:$=1$ to $\frac{n}{2}$ :

$A[i]$:$=A[i]+i$;

function $(A[1..\frac{n}{2}])$;

$\}$

a$)(4$p$)$Express the Time complexity of above algorithm as a recurrence

b$)(5$p$)$Find the closed form of recurrence by using substitution, iteration method or recursion tree method.