Solve S_{4}=2(a_{3}+1)

$$S _ { 4 } = 2 ( a _ { 3 } + 1 )$$

Solve for a_3

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

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by a_{3}+1.

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

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

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

Subtract 2 from both sides.

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide S_{4}-2 by 2.

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

Solve for S_4

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

Solution Steps

Use the distributive property to multiply 2 by a_{3}+1.

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