an = 3an-1, if a1 = 2. 

We check to see if it is a geometric sequence.

r = 

Divide both sides of 

an = 3an-1 

by an-1,

 =  =  = 3

and since r = , it is a geometric series with r = 3

an = a1rn-1

Substitute 4375 for an and 2 for a1

4375 = 2(3n-1)

Divide both sides by 2

2187.5 = 3n-1

Take logs of both sides"

log(2187.5) = log(3n-1)

log(2187.5) = (n-1)log(3)

 = n-1

7.000208078 = n-1
8.000208-78 = n

That did not come out a whole number, 
so the problem is botched.  The 8th term is

an = a1rn-1

Substitute a1 = 2; n=8; r=3:


a8 = 2·38-1

a8 = 2·37

a8 = 4374

So you copied the problem wrong. 
It should have been 4,374,  not 4375.

-----------------------------------------

So change the problem from 4375 to 4374.

an = a1rn-1

Substitute 4374 for an and 2 for a1

4374 = 2(3n-1)

Divide both sides by 2

2187 = 3n-1

Take logs of both sides"

log(2187) = log(3n-1)

log(2187) = (n-1)log(3)

 = n-1

7 = n-1
8 = n

So 4374 is the 8th term.

Edwin