Question

Find two geometric means between 7 and 189

Answer 1

Answer:   21, 63

Step-by-step explanation:

We need to find two geometric means between 7 and 189.

The Geometric Sequence is: 7, ____, ____, 189

Let's find r (common ratio):

We can see that the common ratio will be multiplied by itsely 3 times in order to get from 7 to 189:

                                           7 r³ = 189

                                            $r^3=\dfrac{189}{7}$

                                            r³ = 27

                                          ∛r³ = ∛27

                                              r = 3

Now that we know the common ratio is 3, we can multiply 7 and 3 to get the next term (21), and multiply that by 3 to get the third term (63), and multiply that by 3 as a check to confirm we get 189.

7 x 3 = 21

           21 x 3 = 63

                         63 x 3 = 189 $\checkmark$

The completed Geometric Sequence is: 7, 21,  63, 189