Solve a_{n}=3n/1+6n

$$a _ { n } = \frac { 3 n } { 1 + 6 n }$$

Solve for n

$$n=\frac{a_{n}}{3\left(1-2a_{n}\right)}$$

$$a_{n}\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Variable n cannot be equal to -\frac{1}{6} since division by zero is not defined. Multiply both sides of the equation by 6n+1.

$$a_{n}\left(6n+1\right)=3n$$

Use the distributive property to multiply a_{n} by 6n+1.

$$6a_{n}n+a_{n}=3n$$

Subtract 3n from both sides.

$$6a_{n}n+a_{n}-3n=0$$

Subtract a_{n} from both sides. Anything subtracted from zero gives its negation.

$$6a_{n}n-3n=-a_{n}$$

Combine all terms containing n.

$$\left(6a_{n}-3\right)n=-a_{n}$$

Divide both sides by 6a_{n}-3.

$$\frac{\left(6a_{n}-3\right)n}{6a_{n}-3}=-\frac{a_{n}}{6a_{n}-3}$$

Dividing by 6a_{n}-3 undoes the multiplication by 6a_{n}-3.

$$n=-\frac{a_{n}}{6a_{n}-3}$$

Divide -a_{n} by 6a_{n}-3.

$$n=-\frac{a_{n}}{3\left(2a_{n}-1\right)}$$

Variable n cannot be equal to -\frac{1}{6}.

$$n=-\frac{a_{n}}{3\left(2a_{n}-1\right)}\text{, }n\neq -\frac{1}{6}$$

Solve for a_n

$$a_{n}=\frac{3n}{6n+1}$$

$$n\neq -\frac{1}{6}$$