Solve 363=a(1-(1/3)^5)/1-frac{1{3}}

$$363 = \frac { a ( 1 - ( \frac { 1 } { 3 } ) ^ { 5 } ) } { 1 - \frac { 1 } { 3 } }$$

Solve for a

$$a=243$$

Steps for Solving Linear Equation

Calculate \frac{1}{3} to the power of 5 and get \frac{1}{243}.

$$363=\frac{a\left(1-\frac{1}{243}\right)}{1-\frac{1}{3}}$$

Convert 1 to fraction \frac{243}{243}.

$$363=\frac{a\left(\frac{243}{243}-\frac{1}{243}\right)}{1-\frac{1}{3}}$$

Since \frac{243}{243} and \frac{1}{243} have the same denominator, subtract them by subtracting their numerators.

$$363=\frac{a\times \frac{243-1}{243}}{1-\frac{1}{3}}$$

Subtract 1 from 243 to get 242.

$$363=\frac{a\times \frac{242}{243}}{1-\frac{1}{3}}$$

Convert 1 to fraction \frac{3}{3}.

$$363=\frac{a\times \frac{242}{243}}{\frac{3}{3}-\frac{1}{3}}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$363=\frac{a\times \frac{242}{243}}{\frac{3-1}{3}}$$

Subtract 1 from 3 to get 2.

$$363=\frac{a\times \frac{242}{243}}{\frac{2}{3}}$$

Divide a\times \frac{242}{243} by \frac{2}{3} to get a\times \frac{121}{81}.

$$363=a\times \frac{121}{81}$$

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

$$a\times \frac{121}{81}=363$$

Multiply both sides by \frac{81}{121}, the reciprocal of \frac{121}{81}.

$$a=363\times \frac{81}{121}$$

Express 363\times \frac{81}{121} as a single fraction.

$$a=\frac{363\times 81}{121}$$

Multiply 363 and 81 to get 29403.

$$a=\frac{29403}{121}$$

Divide 29403 by 121 to get 243.

$$a=243$$