Solve a_{n}=11/8+1/2(n-1)

$$a _ { n } = \frac { 11 } { 8 } + \frac { 1 } { 2 } ( n - 1 )$$

Solve for a_n

$$a_{n}=\frac{n}{2}+\frac{7}{8}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by n-1.

$$a_{n}=\frac{11}{8}+\frac{1}{2}n-\frac{1}{2}$$

Subtract \frac{1}{2} from \frac{11}{8} to get \frac{7}{8}.

$$a_{n}=\frac{7}{8}+\frac{1}{2}n$$

Solve for n

$$n=2a_{n}-\frac{7}{4}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by n-1.

$$a_{n}=\frac{11}{8}+\frac{1}{2}n-\frac{1}{2}$$

Subtract \frac{1}{2} from \frac{11}{8} to get \frac{7}{8}.

$$a_{n}=\frac{7}{8}+\frac{1}{2}n$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{7}{8}+\frac{1}{2}n=a_{n}$$

Subtract \frac{7}{8} from both sides.

$$\frac{1}{2}n=a_{n}-\frac{7}{8}$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}n}{\frac{1}{2}}=\frac{a_{n}-\frac{7}{8}}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$n=\frac{a_{n}-\frac{7}{8}}{\frac{1}{2}}$$

Divide a_{n}-\frac{7}{8} by \frac{1}{2} by multiplying a_{n}-\frac{7}{8} by the reciprocal of \frac{1}{2}.

$$n=2a_{n}-\frac{7}{4}$$