Whakaoti i te {l}{5250=11/2[2a+(n-1)(-15)]}{6500=n[610+(n-1)(-15)}

$$\left. \begin{array} { l } { 5250 = \frac { 11 } { 2 } [ 2 a + ( n - 1 ) ( - 15 ) ] } \\ { 6500 = n [ 610 + ( n - 1 ) ( - 15 ) } \end{array} \right.$$

Whakaoti mō a, n

$$a = \frac{1082835}{22} = 49219\frac{17}{22} \approx 49219.772727273$$

$$n=6500$$

Ngā Upane Otinga

Whakaarohia te whārite tuarua. Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$n=6500$$

Whakaarohia te whārite tuatahi. Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$5250=\frac{11}{2}\left(2a+\left(6500-1\right)\left(-15\right)\right)$$

Me whakarea ngā taha e rua ki te \frac{2}{11}, te tau utu o \frac{11}{2}.

$$5250\times \frac{2}{11}=2a+\left(6500-1\right)\left(-15\right)$$

Whakareatia te 5250 ki te \frac{2}{11}, ka \frac{10500}{11}.

$$\frac{10500}{11}=2a+\left(6500-1\right)\left(-15\right)$$

Tangohia te 1 i te 6500, ka 6499.

$$\frac{10500}{11}=2a+6499\left(-15\right)$$

Whakareatia te 6499 ki te -15, ka -97485.

$$\frac{10500}{11}=2a-97485$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$2a-97485=\frac{10500}{11}$$

Me tāpiri te 97485 ki ngā taha e rua.

$$2a=\frac{10500}{11}+97485$$

Tāpirihia te \frac{10500}{11} ki te 97485, ka \frac{1082835}{11}.

$$2a=\frac{1082835}{11}$$

Whakawehea ngā taha e rua ki te 2.

$$a=\frac{\frac{1082835}{11}}{2}$$

Tuhia te \frac{\frac{1082835}{11}}{2} hei hautanga kotahi.

$$a=\frac{1082835}{11\times 2}$$

Whakareatia te 11 ki te 2, ka 22.

$$a=\frac{1082835}{22}$$

Kua oti te pūnaha te whakatau.

$$a=\frac{1082835}{22} n=6500$$