Solve a_{4}=2a_{3}+2

$$a _ { 4 } = 2 a _ { 3 } + 2$$

Solve for a_3

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

Steps for Solving Linear Equation

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

$$2a_{3}+2=a_{4}$$

Subtract 2 from both sides.

$$2a_{3}=a_{4}-2$$

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide a_{4}-2 by 2.

$$a_{3}=\frac{a_{4}}{2}-1$$

Solve for a_4

$$a_{4}=2\left(a_{3}+1\right)$$