Question

What is the tenth term of the geometric sequence that has a common ratio of `1/3` and 36 as its fifth term?

Answer 1

`\bf \begin{array}{llll} term&value\\ \cline{1-2} a_5&36\\ a_6&36\left( (1)/(3) \right)\\ a_7&36\left( (1)/(3) \right)\left( (1)/(3) \right)\\ a_8&36\left( (1)/(3) \right)\left( (1)/(3) \right)\left( (1)/(3) \right)\\ a_9&36\left( (1)/(3) \right)\left( (1)/(3) \right)\left( (1)/(3) \right)\left( (1)/(3) \right)\\ a_(10)&36\left( (1)/(3) \right)\left( (1)/(3) \right)\left( (1)/(3) \right)\left( (1)/(3) \right)\left( (1)/(3) \right) \end{array}`

`\bf a_(10)=36\left( (1)/(3) \right)^5\implies a_(10)=36\cdot \cfrac{1^5}{3^5}\implies a_(10)=\cfrac{36}{243}\implies a_(10)=\cfrac{4}{27}`