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

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

d खातीर सोडोवचें

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

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

लिनियर समिकरण सोडोवंक पांवडे

दोनूय कुशीनीं 2 न गुणचें.

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

10 मेळोवंक 5 आनी 5 ची बेरीज करची.

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

d न n-1 गुणपाक विभाजक विशमाचो वापर करचो.

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

n न 10+nd-d गुणपाक विभाजक विशमाचो वापर करचो.

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

780 मेळोवंक 390 आनी 2 गुणचें.

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

दोनूय कुशींतल्यान 10n वजा करचें.

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

d आसपी सगळ्यो संज्ञा एकठांय करच्यो.

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

दोनुय कुशींक n^{2}-n न भाग लावचो.

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

n^{2}-n वरवीं भागाकार केल्यार n^{2}-n वरवीं केल्लो गुणाकार काडटा.

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

n^{2}-n न780-10n क भाग लावचो.

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

n खातीर सोडोवचें (जटील सोल्यूशन)

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

n खातीर सोडोवचें

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