a5=a2q^3
162=6q^3
q^3=27
q=3
a2=a1q
6=a1*3
a1=2
an=a1q^(n-1)
=2*3^(n-1)
sn=a1(1-q^n)/(1-q)
=2*(1-3^n)/(1-3)
=3^n-1
Sn>50
3^n-1>50
3^n>51
3^4>51>3^3
n>3
所以数列{a(n)}的前n项和Sn>50,n的最小值是：4