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

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

Solve for a_n

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

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

Use the distributive property to multiply n by 2n+1.

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

Divide both sides by 14.

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

Dividing by 14 undoes the multiplication by 14.

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

Solve for n

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

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