Whakaoti i te n/2{2a+(n-1)d}=106200

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

Whakaoti mō a

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

$$n\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te 2.

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

Whakamahia te āhuatanga tohatoha hei whakarea te n-1 ki te d.

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

Whakamahia te āhuatanga tohatoha hei whakarea te n ki te 2a+nd-d.

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

Tangohia te dn^{2} mai i ngā taha e rua.

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

Me tāpiri te nd ki ngā taha e rua.

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

Whakaraupapatia anō ngā kīanga tau.

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te 2n.

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

Mā te whakawehe ki te 2n ka wetekia te whakareanga ki te 2n.

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

Whakawehe -dn^{2}+dn+212400 ki te 2n.

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

Whakaoti mō d

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te 2.

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

Whakamahia te āhuatanga tohatoha hei whakarea te n-1 ki te d.

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

Whakamahia te āhuatanga tohatoha hei whakarea te n ki te 2a+nd-d.

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

Tangohia te 2na mai i ngā taha e rua.

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

Pahekotia ngā kīanga tau katoa e whai ana i te d.

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te n^{2}-n.

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

Mā te whakawehe ki te n^{2}-n ka wetekia te whakareanga ki te n^{2}-n.

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

Whakawehe 212400-2na ki te n^{2}-n.

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