an=2(an-1)+(an-2)

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Solution for an=2(an-1)+(an-2) equation: 


Simplifying
an = 2(an + -1) + (an + -2)

Reorder the terms:
an = 2(-1 + an) + (an + -2)
an = (-1 * 2 + an * 2) + (an + -2)
an = (-2 + 2an) + (an + -2)

Reorder the terms:
an = -2 + 2an + (-2 + an)

Remove parenthesis around (-2 + an)
an = -2 + 2an + -2 + an

Reorder the terms:
an = -2 + -2 + 2an + an

Combine like terms: -2 + -2 = -4
an = -4 + 2an + an

Combine like terms: 2an + an = 3an
an = -4 + 3an

Solving
an = -4 + 3an

Solving for variable 'a'.

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

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

Combine like terms: an + -3an = -2an
-2an = -4 + 3an + -3an

Combine like terms: 3an + -3an = 0
-2an = -4 + 0
-2an = -4

Divide each side by '-2n'.
a = 2n-1

Simplifying
a = 2n-1

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