Réitigh left(5+5+left(n-1right)dright)n/2=390

$$\frac{ \left( 5+5+ \left( n-1 \right) d \right) n }{ 2 } =390$$

Réitigh do d.

$$d=-\frac{10\left(n-78\right)}{n\left(n-1\right)}$$

$$n\neq 1\text{ and }n\neq 0$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Iolraigh an dá thaobh faoi 2.

$$\left(5+5+\left(n-1\right)d\right)n=390\times 2$$

Suimigh 5 agus 5 chun 10 a fháil.

$$\left(10+\left(n-1\right)d\right)n=390\times 2$$

Úsáid an t-airí dáileach chun n-1 a mhéadú faoi d.

$$\left(10+nd-d\right)n=390\times 2$$

Úsáid an t-airí dáileach chun 10+nd-d a mhéadú faoi n.

$$10n+dn^{2}-dn=390\times 2$$

Méadaigh 390 agus 2 chun 780 a fháil.

$$10n+dn^{2}-dn=780$$

Bain 10n ón dá thaobh.

$$dn^{2}-dn=780-10n$$

Comhcheangail na téarmaí ar fad ina bhfuil d.

$$\left(n^{2}-n\right)d=780-10n$$

Roinn an dá thaobh faoi n^{2}-n.

$$\frac{\left(n^{2}-n\right)d}{n^{2}-n}=\frac{780-10n}{n^{2}-n}$$

Má roinntear é faoi n^{2}-n cuirtear an iolrúchán faoi n^{2}-n ar ceal.

$$d=\frac{780-10n}{n^{2}-n}$$

Roinn 780-10n faoi n^{2}-n.

$$d=\frac{10\left(78-n\right)}{n\left(n-1\right)}$$

Réitigh do n. (complex solution)

$$\left\{\begin{matrix}n=\frac{\sqrt{d^{2}+3100d+100}+d-10}{2d}\text{; }n=\frac{-\sqrt{d^{2}+3100d+100}+d-10}{2d}\text{, }&d\neq 0\\n=78\text{, }&d=0\end{matrix}\right.$$

Réitigh do n.

$$\left\{\begin{matrix}n=\frac{\sqrt{d^{2}+3100d+100}+d-10}{2d}\text{; }n=\frac{-\sqrt{d^{2}+3100d+100}+d-10}{2d}\text{, }&d\leq -20\sqrt{6006}-1550\text{ or }\left(d\neq 0\text{ and }d\geq 20\sqrt{6006}-1550\right)\\n=78\text{, }&d=0\end{matrix}\right.$$