we have that
6,18,54,162,...
we know that
a1=6
a2=18
a3=54
a4=162
a2/a1=18/6--------> 3
a3/a2=54/18-------> 3
a4/a3=162/54------> 3
therefore
a(n+1)=an*3
a1=6
for n=1
a(1+1)=a1*3---------> a2=a1*3--------> a2=6*3------> a2=18
for n=2
a(2+1)=a2*3---------> a3=a2*3--------> a3=18*3------> a3=54
for n=3
a(3+1)=a3*3---------> a4=a3*3--------> a4=54*3------> a4=162
therefore
the equation for the sequence is
a(n+1)=an*3
