Solve 1/254.5=a0/1+a_{0(20)}

$$\frac { 1 } { 254.5 } = \frac { a 0 } { 1 + a _ { 0 } ( 20 ) }$$

Solve for a_0

$$a_{0}=\frac{2}{469}\approx 0.004264392$$

Steps for Solving Linear Equation

Variable a_{0} cannot be equal to -\frac{1}{20} since division by zero is not defined. Multiply both sides of the equation by 20a_{0}+1.

$$\left(20a_{0}+1\right)\times \frac{1}{254.5}=a_{0}$$

Expand \frac{1}{254.5} by multiplying both numerator and the denominator by 10.

$$\left(20a_{0}+1\right)\times \frac{10}{2545}=a_{0}$$

Reduce the fraction \frac{10}{2545} to lowest terms by extracting and canceling out 5.

$$\left(20a_{0}+1\right)\times \frac{2}{509}=a_{0}$$

Use the distributive property to multiply 20a_{0}+1 by \frac{2}{509}.

$$\frac{40}{509}a_{0}+\frac{2}{509}=a_{0}$$

Subtract a_{0} from both sides.

$$\frac{40}{509}a_{0}+\frac{2}{509}-a_{0}=0$$

Combine \frac{40}{509}a_{0} and -a_{0} to get -\frac{469}{509}a_{0}.

$$-\frac{469}{509}a_{0}+\frac{2}{509}=0$$

Subtract \frac{2}{509} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{469}{509}a_{0}=-\frac{2}{509}$$

Multiply both sides by -\frac{509}{469}, the reciprocal of -\frac{469}{509}.

$$a_{0}=-\frac{2}{509}\left(-\frac{509}{469}\right)$$

Multiply -\frac{2}{509} and -\frac{509}{469} to get \frac{2}{469}.

$$a_{0}=\frac{2}{469}$$