Solve T_{1}=2b+1(-1^n-1)

$$T _ { 1 } = 2 b + 1 ( - 1 ^ { n - 1 } )$$

Solve for b

$$b=\frac{T_{1}+1}{2}$$

Steps for Solving Linear Equation

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

$$2b+1\left(-1^{n-1}\right)=T_{1}$$

Subtract 1\left(-1^{n-1}\right) from both sides.

$$2b=T_{1}-1\left(-1^{n-1}\right)$$

Reorder the terms.

$$2b=T_{1}-\left(-1^{n-1}\right)$$

Multiply -1 and -1 to get 1.

$$2b=T_{1}+1^{n-1}$$

The equation is in standard form.

$$2b=T_{1}+1$$

Divide both sides by 2.

$$\frac{2b}{2}=\frac{T_{1}+1}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$b=\frac{T_{1}+1}{2}$$

Solve for T_1

$$T_{1}=2b-1$$