Solve {l}{a_{n}=-3(n-1)/3-2n}{n=5}

$$\left\{ \begin{array} { l } { a _ { n } = - \frac { 3 ( n - 1 ) } { 3 - 2 n } } \\ { n = 5 } \end{array} \right.$$

Solve for a_n, n

$$a_{n} = \frac{12}{7} = 1\frac{5}{7} \approx 1.714285714$$

$$n=5$$

Solution Steps

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

$$a_{n}=-\frac{3\left(5-1\right)}{3-2\times 5}$$

Subtract 1 from 5 to get 4.

$$a_{n}=-\frac{3\times 4}{3-2\times 5}$$

Multiply 3 and 4 to get 12.

$$a_{n}=-\frac{12}{3-2\times 5}$$

Multiply -2 and 5 to get -10.

$$a_{n}=-\frac{12}{3-10}$$

Subtract 10 from 3 to get -7.

$$a_{n}=-\frac{12}{-7}$$

Fraction \frac{12}{-7} can be rewritten as -\frac{12}{7} by extracting the negative sign.

$$a_{n}=-\left(-\frac{12}{7}\right)$$

The opposite of -\frac{12}{7} is \frac{12}{7}.

$$a_{n}=\frac{12}{7}$$

The system is now solved.

$$a_{n}=\frac{12}{7} n=5$$