Question

Insert 2 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  $r^{3}$= 189

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

                                         $r^{3}$  = 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  

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