Solve a_{n}=(n+1)(n-2)

$$a _ { n } = ( n + 1 ) ( n - 2 )$$

Solve for a_n

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

Solution Steps

Use the distributive property to multiply n+1 by n-2 and combine like terms.

$$a_{n}=n^{2}-n-2$$

Solve for n (complex solution)

$$n=\frac{-\sqrt{4a_{n}+9}+1}{2}$$

$$n=\frac{\sqrt{4a_{n}+9}+1}{2}$$

Solve for n

$$n=\frac{-\sqrt{4a_{n}+9}+1}{2}$$

$$n=\frac{\sqrt{4a_{n}+9}+1}{2}\text{, }a_{n}\geq -\frac{9}{4}$$