Question

Which choice is the explicit formula for the following geometric sequence?0.5, -0.1, 0.02, -0.004, 0.0008, ...

Answer 1

`a_1=0.5\\a_2=-0.1\\a_3=0.02\\a_4=-0.004\\a_5=0.0008\\\\a_n=a_1\cdot q^(n-1)\\\\q=a_2:a_1\to q=-0.1:0.5=-0.2\\\\a_n=0.5\cdot(-0.2)^(n-1)=0.5\cdot(-0,2)^n\cdot(-0.2)^(-1)\\\\=0.5\cdot(-0.2)^n\cdot(-5)=-2.5\cdot(-0.2)^n\\\\\boxed{a_n=-2.5\cdot(-0.2)^n}`