Question

How do u solve this?

Answer 1

`\large\boxed{\left\{\begin{array}{ccc}f(1)=5\\f(n)=f(n-1)\cdot(-2)\end{array}\right}`

Explanation:

`f(n)=5\cdot(-2)^(n-1)\\\\f(1)\to\text{put n = 1 to the equation of}\ f(n):\\\\f(1)=5\cdcot(-2)^(1-1)=5\cdot(-2)^0=5\cdot1=5\\\\\text{calculate the common ratio:}\ (f(n+1))/(f(n))\\\\f(n+1)=5\cdot(-2)^((n+1)-1)=5\cdot(-2)^(n+1-1)=5\cdot(-2)^n\\\\r=(f(n+1))/(f(n))=(5\!\!\!\!\diagup^1\cdot(-2)^n)/(5\!\!\!\!\diagup_1\cdot(-2)^(n-1))\qquad\text{use}\ (a^m)/(a^n)=a^(m-n)\\\\r=(-2)^(n-(n-1))=(-2)^(n-n+1)=(-2)^1=-2\\\\\text{Therefore}\\\\f(n)=f(n-1)\cdiot(-2)`