Question

What is the 6th term of the geometric sequence f(1) = 12, f(n) = -2/3f(n-1)

Answer 1

`\bf \begin{array}{ccll} \stackrel{n^(th)}{term}&value\\\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\\\ 1&12\\\\ 2&-(2)/(3)f(2-1)\\\\ &-(2)/(3)f(1)\\\\ &-(2)/(3)(12)\\\\ &-8\\\\ 3&-(2)/(3)f(3-1)\\\\ &-(2)/(3)f(2)\\\\ &-(2)/(3)(-8)\\\\ &(16)/(3) \end{array}`


`\bf \begin{array}{cccl} \qquad &\qquad \\ 4&-(2)/(3)f(4-1)\\\\ &-(2)/(3)f(3)\\\\ &-(2)/(3)\left( (16)/(3) \right)\\\\ &-(32)/(9)\\\\ 5&-(2)/(3)f(5-1)\\\\ &-(2)/(3)f(4)\\\\ &-(2)/(3)\left( -(32)/(9) \right)\\\\ &(64)/(27)\\\\ 6&-(2)/(3)f(6-1)\\\\ &-(2)/(3)f(5)\\\\ &-(2)/(3)\left( (64)/(27)\right) \end{array}`