(an)=3(an-1)+(n)

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Solution for (an)=3(an-1)+(n) equation: 


Simplifying
(an) = 3(an + -1) + (n)
an = 3(an + -1) + (n)

Reorder the terms:
an = 3(-1 + an) + (n)
an = (-1 * 3 + an * 3) + (n)
an = (-3 + 3an) + (n)
an = -3 + 3an + n

Solving
an = -3 + 3an + n

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 = -3 + 3an + -3an + n

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

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

Divide each side by '-2n'.
a = 1.5n-1 + -0.5

Simplifying
a = 1.5n-1 + -0.5

Reorder the terms:
a = -0.5 + 1.5n-1

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