Answer
Geometric sequence with ratio $\dfrac{1}{r}$
Work Step by Step
We are given the geometric sequence:
$$a_1,a_2,a_3,\dots,...$$
where $a_{k+1}=a_kr$.
Consider the sequence:
$$\dfrac{1}{a_1},\dfrac{1}{a_2},\dfrac{1}{a_2},,\dots$$
We calculate the ratio of two consecutive terms:
$$\dfrac{\dfrac{1}{a_{k+1}}}{\dfrac{1}{a_k}}=\dfrac{a_k}{a_{k+1}}=\dfrac{a_k}{a_kr}=\dfrac{1}{r}$$
So the second sequence is also geometric, its common ratio being $\dfrac{1}{r}$.
