Write a explicit equation for the sequence 6,18,54,

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

Where’s the following prism