Find two geometric means between 7 and 189

We have that the two geometric means between 7 and 189 are

From the calculations below

From the question we are told that:

There are two geometric means

7 and 189

Generally for two geometric means between 7 and 189

Let the unknown means be x and y respectively

Therefore

The geometric Progression will be

7,x,y,189

Since they share a similar common ratio r

Therefore

Hence

And

Therefore

Substituting equ1 into equ2 we have

Having x we substitute x into equ...1

In Conclusion

The two geometric means between 7 and 189

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In conclusion

  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

                                            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

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

a = 11 : 4

b = 38

c = 1 for every 6

the functions have the same rate of change i think. i narrowed it down to this answer and "the rate of change of tour 1 is greater" but i got it wrong using that answer so im assuming its the answer above. (this is a question i also answered from the iready site if anyone needs a reference)