Question

What is the value of the fourth term in a geometric sequence for which a1= 15 and r= 1/3

Answer 1

`\bf \begin{array}{cll} term&value\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ a_1&15\\ a_2&15\left( (1)/(3) \right)\\\\ a_3&15\left( (1)/(3) \right)\left( (1)/(3) \right)\\\\ a_4&15\left( (1)/(3) \right)\left( (1)/(3) \right)\left( (1)/(3) \right) \end{array}\qquad \implies 15\left( (1)/(3) \right)^3\implies 15\cdot \cfrac{1^3}{3^3} \\\\\\ \cfrac{15}{27}\implies \stackrel{simplified}{\cfrac{5}{9}}`