7*a_{n}=n(2n+1)/2 eching

$$7 \cdot a _ { n } = \frac { n ( 2 n + 1 ) } { 2 }$$

a_n uchun yechish

$$a_{n}=\frac{n\left(2n+1\right)}{14}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$14a_{n}=n\left(2n+1\right)$$

n ga 2n+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$14a_{n}=2n^{2}+n$$

Ikki tarafini 14 ga bo‘ling.

$$\frac{14a_{n}}{14}=\frac{n\left(2n+1\right)}{14}$$

14 ga bo'lish 14 ga ko'paytirishni bekor qiladi.

$$a_{n}=\frac{n\left(2n+1\right)}{14}$$

n uchun yechish

$$n=\frac{\sqrt{112a_{n}+1}-1}{4}$$

$$n=\frac{-\sqrt{112a_{n}+1}-1}{4}\text{, }a_{n}\geq -\frac{1}{112}$$