Question

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

Answer 1

`\bf \begin{array}{cll} term&value\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ a_5&36\\ a_6&36\cdot (1)/(3)\\\\ a_7&\left( 36\cdot (1)/(3) \right)(1)/(3)\\\\ a_8&\left( 36\cdot (1)/(3)\cdot (1)/(3) \right)(1)/(3)\\\\ a_9&\left( 36\cdot (1)/(3)\cdot (1)/(3)\cdot (1)/(3) \right)(1)/(3)\\\\ a_(10)&\left( 36\cdot (1)/(3)\cdot (1)/(3)\cdot (1)/(3)\cdot (1)/(3) \right)(1)/(3) \end{array}`


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