For the following geometric sequence, find the recursive formula. {-80, 20, -5, …}

For the following geometric sequence, find the recursive formula. (-80,20,-5…)

Answer:

For the geometric sequence, it has two forms of formula

We are interested in the recursive formula now

{-80, 20, -5, …}

The common ratio is (20/-80)=(-5/20)=-1/4=-0.25

So our recursive formula would bea_n=a_{n-1}*(-0.25)=a_{n-1}*(- \frac{1}{4} )an=an−1∗(−0.25)=an−1∗(−41)