Solve 2(1+a_{2})=a_{1}+a_{3}

$$2 ( 1 + a _ { 2 } ) = a _ { 1 } + a _ { 3 }$$

Solve for a_1

$$a_{1}=2a_{2}-a_{3}+2$$

Solution Steps

Use the distributive property to multiply 2 by 1+a_{2}.

$$2+2a_{2}=a_{1}+a_{3}$$

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

$$a_{1}+a_{3}=2+2a_{2}$$

Subtract a_{3} from both sides.

$$a_{1}=2+2a_{2}-a_{3}$$

Solve for a_2

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

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 1+a_{2}.

$$2+2a_{2}=a_{1}+a_{3}$$

Subtract 2 from both sides.

$$2a_{2}=a_{1}+a_{3}-2$$

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide a_{1}+a_{3}-2 by 2.

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