Solve {l}{a_{n}=-3(n-1)/3-2n}{n=4}

$$\left\{ \begin{array} { l } { a _ { n } = - \frac { 3 ( n - 1 ) } { 3 - 2 n } } \\ { n = 4 } \end{array} \right.$$

Solve for a_n, n

$$a_{n} = \frac{9}{5} = 1\frac{4}{5} = 1.8$$

$$n=4$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$a_{n}=-\frac{3\left(4-1\right)}{3-2\times 4}$$

Subtract 1 from 4 to get 3.

$$a_{n}=-\frac{3\times 3}{3-2\times 4}$$

Multiply 3 and 3 to get 9.

$$a_{n}=-\frac{9}{3-2\times 4}$$

Multiply -2 and 4 to get -8.

$$a_{n}=-\frac{9}{3-8}$$

Subtract 8 from 3 to get -5.

$$a_{n}=-\frac{9}{-5}$$

Fraction \frac{9}{-5} can be rewritten as -\frac{9}{5} by extracting the negative sign.

$$a_{n}=-\left(-\frac{9}{5}\right)$$

The opposite of -\frac{9}{5} is \frac{9}{5}.

$$a_{n}=\frac{9}{5}$$

The system is now solved.

$$a_{n}=\frac{9}{5} n=4$$