Answer
a) 76
b) 48829
c) 30517579
Work Step by Step
We are given
$$f(n)=f(n/5)+3n^2$$
and $$f(1)=4$$
a) Apply the recurrence relation when $n=5$
$f(5)=f(1)+ 3\times5^2$
$=1+75$
$=76$
b) Apply the recurrence relation when $n=25$
$f(25)=f(5)+ 3\times25^2$
$=79+1875$
$=1954$
$f(125)=f(25)+ 3\times125^2$
$=1954+46875$
$=48829$
c) Apply the recurrence relation when $n=3125$
First $f(625)=f(125)+ 3 \times 625^2$
$=48829+1171875$
$=1220704$
$f(3125)=f(625)+ 3\times3125^2$
$=1220704+29296875$
$=30517579$
