Solve n/2{2a+(n-1)d}=106200

$$\frac { n } { 2 } \{ 2 a + ( n - 1 ) d \} = 106200$$

Solve for a

$$a=-\frac{dn}{2}+\frac{d}{2}+\frac{106200}{n}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$n\left(2a+\left(n-1\right)d\right)=212400$$

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

$$n\left(2a+nd-d\right)=212400$$

Use the distributive property to multiply n by 2a+nd-d.

$$2na+dn^{2}-nd=212400$$

Subtract dn^{2} from both sides.

$$2na-nd=212400-dn^{2}$$

Add nd to both sides.

$$2na=212400-dn^{2}+nd$$

Reorder the terms.

$$2an=-dn^{2}+dn+212400$$

The equation is in standard form.

$$2na=212400+dn-dn^{2}$$

Divide both sides by 2n.

$$\frac{2na}{2n}=\frac{212400+dn-dn^{2}}{2n}$$

Dividing by 2n undoes the multiplication by 2n.

$$a=\frac{212400+dn-dn^{2}}{2n}$$

Divide -dn^{2}+dn+212400 by 2n.

$$a=-\frac{dn}{2}+\frac{d}{2}+\frac{106200}{n}$$

Solve for d

$$\left\{\begin{matrix}d=-\frac{2\left(an-106200\right)}{n\left(n-1\right)}\text{, }&n\neq 1\text{ and }n\neq 0\\d\in \mathrm{R}\text{, }&a=106200\text{ and }n=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$n\left(2a+\left(n-1\right)d\right)=212400$$

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

$$n\left(2a+nd-d\right)=212400$$

Use the distributive property to multiply n by 2a+nd-d.

$$2na+dn^{2}-nd=212400$$

Subtract 2na from both sides.

$$dn^{2}-nd=212400-2na$$

Combine all terms containing d.

$$\left(n^{2}-n\right)d=212400-2na$$

The equation is in standard form.

$$\left(n^{2}-n\right)d=212400-2an$$

Divide both sides by n^{2}-n.

$$\frac{\left(n^{2}-n\right)d}{n^{2}-n}=\frac{212400-2an}{n^{2}-n}$$

Dividing by n^{2}-n undoes the multiplication by n^{2}-n.

$$d=\frac{212400-2an}{n^{2}-n}$$

Divide 212400-2na by n^{2}-n.

$$d=\frac{2\left(106200-an\right)}{n\left(n-1\right)}$$