Solve an=a_{1}+(n-1)

$$a n = a _ { 1 } + ( n - 1 )$$

Solve for a

$$\left\{\begin{matrix}a=\frac{n+a_{1}-1}{n}\text{, }&n\neq 0\\a\in \mathrm{R}\text{, }&n=0\text{ and }a_{1}=1\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$na=n+a_{1}-1$$

Divide both sides by n.

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

Dividing by n undoes the multiplication by n.

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

Solve for a_1

$$a_{1}=an-n+1$$

Solution Steps

Swap sides so that all variable terms are on the left hand side.

$$a_{1}+n-1=an$$

Subtract n from both sides.

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

Add 1 to both sides.

$$a_{1}=an-n+1$$