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

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

Solve for a

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

Steps for Solving Linear Equation

Use the distributive property to multiply n-1 by a.

$$an=a_{1}+\left(na-a\right)s$$

Use the distributive property to multiply na-a by s.

$$an=a_{1}+nas-as$$

Subtract nas from both sides.

$$an-nas=a_{1}-as$$

Add as to both sides.

$$an-nas+as=a_{1}$$

Reorder the terms.

$$-ans+an+as=a_{1}$$

Combine all terms containing a.

$$\left(-ns+n+s\right)a=a_{1}$$

The equation is in standard form.

$$\left(s+n-ns\right)a=a_{1}$$

Divide both sides by n-sn+s.

$$\frac{\left(s+n-ns\right)a}{s+n-ns}=\frac{a_{1}}{s+n-ns}$$

Dividing by n-sn+s undoes the multiplication by n-sn+s.

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

Solve for a_1

$$a_{1}=a\left(s+n-ns\right)$$