An=3An-1+An-2

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Solution for An=3An-1+An-2 equation: 


Simplifying
An = 3An + -1 + An + -2

Reorder the terms:
nA = -1 + -2 + 3nA + nA

Combine like terms: -1 + -2 = -3
nA = -3 + 3nA + nA

Combine like terms: 3nA + nA = 4nA
nA = -3 + 4nA

Solving
nA = -3 + 4nA

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-4nA' to each side of the equation.
nA + -4nA = -3 + 4nA + -4nA

Combine like terms: nA + -4nA = -3nA
-3nA = -3 + 4nA + -4nA

Combine like terms: 4nA + -4nA = 0
-3nA = -3 + 0
-3nA = -3

Divide each side by '-3A'.
n = A-1

Simplifying
n = A-1

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