Answer: [tex]3^{rd}[/tex] term of the given sequence is -320.
Step-by-step explanation:
Given sequence : [tex]b(n)=b(n-1)\cdot\dfrac{4}{5}[/tex] , b(1)=−500
For n =2,
[tex]b(2) =b(1)\cdot\dfrac45=-500\cdot \dfrac45\\\\=-100\cdot4\\\\=-400[/tex]
For n = 3
[tex]b(3) =b(2)\cdot\dfrac45=-400\cdot \dfrac45\\\\=-80\cdot4\\\\=-320[/tex]
So, [tex]3^{rd}[/tex] term of the given sequence is -320.
