Solve l=a+(n-1)d

$$l = a + ( n - 1 ) d$$

Solve for a

$$a=l+d-dn$$

Solution Steps

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

$$l=a+nd-d$$

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

$$a+nd-d=l$$

Subtract nd from both sides.

$$a-d=l-nd$$

Add d to both sides.

$$a=l-nd+d$$

Solve for d

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

Steps for Solving Linear Equation

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

$$l=a+nd-d$$

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

$$a+nd-d=l$$

Subtract a from both sides.

$$nd-d=l-a$$

Combine all terms containing d.

$$\left(n-1\right)d=l-a$$

Divide both sides by n-1.

$$\frac{\left(n-1\right)d}{n-1}=\frac{l-a}{n-1}$$

Dividing by n-1 undoes the multiplication by n-1.

$$d=\frac{l-a}{n-1}$$