Solve 700=frac{a_{1}-a_{1}(1/2)^7}{1-1/2}

$$700 = \frac { a _ { 1 } - a _ { 1 } ( \frac { 1 } { 2 } ) ^ { 7 } } { 1 - \frac { 1 } { 2 } }$$

Solve for a_1

$$a_{1} = \frac{44800}{127} = 352\frac{96}{127} \approx 352.755905512$$

Steps for Solving Linear Equation

Calculate \frac{1}{2} to the power of 7 and get \frac{1}{128}.

$$700=\frac{a_{1}-a_{1}\times \frac{1}{128}}{1-\frac{1}{2}}$$

Combine a_{1} and -a_{1}\times \frac{1}{128} to get \frac{127}{128}a_{1}.

$$700=\frac{\frac{127}{128}a_{1}}{1-\frac{1}{2}}$$

Convert 1 to fraction \frac{2}{2}.

$$700=\frac{\frac{127}{128}a_{1}}{\frac{2}{2}-\frac{1}{2}}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$700=\frac{\frac{127}{128}a_{1}}{\frac{2-1}{2}}$$

Subtract 1 from 2 to get 1.

$$700=\frac{\frac{127}{128}a_{1}}{\frac{1}{2}}$$

Divide \frac{127}{128}a_{1} by \frac{1}{2} to get \frac{127}{64}a_{1}.

$$700=\frac{127}{64}a_{1}$$

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

$$\frac{127}{64}a_{1}=700$$

Multiply both sides by \frac{64}{127}, the reciprocal of \frac{127}{64}.

$$a_{1}=700\times \frac{64}{127}$$

Express 700\times \frac{64}{127} as a single fraction.

$$a_{1}=\frac{700\times 64}{127}$$

Multiply 700 and 64 to get 44800.

$$a_{1}=\frac{44800}{127}$$