Algebra 2 term sequence

Question

A(1)=2, A(n)=3* A(n-1)+4, n>1

Answer 1

A(1) = 2

A(n) = 3A(n-1) + 4, for n = 2, 3, 4, ...

A(2) = 3A(1) + 4 = 10

A(3) = 3A(2) + 4 = 34

A(4) = 3A(3) + 4 = 106, etc

Answer 2

A(n)=(-2/3)3^x+4 is the general solution to this linear difference equation.

I cannot explain here how to obtain this solution except to say that the homogeneous equation has solution C*3^X.

To learn how to obtain the particular solution I refer you to "Calculus of Finite Differences" by Jordan (probably now long out of print but probably available in any good college library).