Solve frac{a_{2}+a_{n}-1}{2}n=1

$$\frac { a _ { 2 } + a _ { n } - 1 } { 2 } n = 1$$

Solve for a_2

$$a_{2}=-a_{n}+1+\frac{2}{n}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

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

Use the distributive property to multiply a_{2}+a_{n}-1 by n.

$$a_{2}n+a_{n}n-n=2$$

Subtract a_{n}n from both sides.

$$a_{2}n-n=2-a_{n}n$$

Add n to both sides.

$$a_{2}n=2-a_{n}n+n$$

The equation is in standard form.

$$na_{2}=2+n-a_{n}n$$

Divide both sides by n.

$$\frac{na_{2}}{n}=\frac{2+n-a_{n}n}{n}$$

Dividing by n undoes the multiplication by n.

$$a_{2}=\frac{2+n-a_{n}n}{n}$$

Divide 2-a_{n}n+n by n.

$$a_{2}=-a_{n}+1+\frac{2}{n}$$

Solve for a_n

$$a_{n}=-a_{2}+1+\frac{2}{n}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

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

Use the distributive property to multiply a_{2}+a_{n}-1 by n.

$$a_{2}n+a_{n}n-n=2$$

Subtract a_{2}n from both sides.

$$a_{n}n-n=2-a_{2}n$$

Add n to both sides.

$$a_{n}n=2-a_{2}n+n$$

The equation is in standard form.

$$na_{n}=2+n-a_{2}n$$

Divide both sides by n.

$$\frac{na_{n}}{n}=\frac{2+n-a_{2}n}{n}$$

Dividing by n undoes the multiplication by n.

$$a_{n}=\frac{2+n-a_{2}n}{n}$$

Divide 2-a_{2}n+n by n.

$$a_{n}=-a_{2}+1+\frac{2}{n}$$