Solve a_{n}=3n+1/n

$$a _ { n } = \frac { 3 n + 1 } { n }$$

Solve for n

$$n=\frac{1}{a_{n}-3}$$

$$a_{n}\neq 3$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by n.

$$a_{n}n=3n+1$$

Subtract 3n from both sides.

$$a_{n}n-3n=1$$

Combine all terms containing n.

$$\left(a_{n}-3\right)n=1$$

Divide both sides by a_{n}-3.

$$\frac{\left(a_{n}-3\right)n}{a_{n}-3}=\frac{1}{a_{n}-3}$$

Dividing by a_{n}-3 undoes the multiplication by a_{n}-3.

$$n=\frac{1}{a_{n}-3}$$

Variable n cannot be equal to 0.

$$n=\frac{1}{a_{n}-3}\text{, }n\neq 0$$

Solve for a_n

$$a_{n}=3+\frac{1}{n}$$

$$n\neq 0$$