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

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

Atrast d

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

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

Lineāra vienādojuma risināšanas darbības

Reiziniet abas puses ar 2.

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

Saskaitiet 5 un 5, lai iegūtu 10.

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

Izmantojiet distributīvo īpašību, lai reizinātu n-1 ar d.

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

Izmantojiet distributīvo īpašību, lai reizinātu 10+nd-d ar n.

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

Reiziniet 390 un 2, lai iegūtu 780.

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

Atņemiet 10n no abām pusēm.

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

Savelciet visus locekļus, kuros ir d.

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

Daliet abas puses ar n^{2}-n.

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

Dalīšana ar n^{2}-n atsauc reizināšanu ar n^{2}-n.

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

Daliet 780-10n ar n^{2}-n.

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

Atrast n

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