Question

find the geometric mean between 3 and 192​

Answer 1

Answer: hopes this one helps you

Step-by-step explanation :The ratio of this geometric progression is 2.

The 5 interpolated terms are:

6 , 12 , 24 , 48 and 96

STEP BY STEP EXPLANATION :

3 , ___ , ___ , ___ , ___ , ___ , 192

An = A1 • [Q^(n - 1)]

192 = 3 • [Q^(7 - 1)]

192 = 3 • [Q^6]

[Q^6] • 3 = 192

[Q^6] = 192/3

[Q^6] = 64

Q =

Q = 2

Answer 2

SOLUTION

TO DETERMINE

The geometric mean between 3 and 192

EVALUATION

Let x be the geometric mean between 3 and 192

Then 3 , x , 192 are in Geometric Progression

So by the given condition

$\displaystyle \sf{ \frac{x}{3} = \frac{192}{x} }$

$\displaystyle \sf{ \implies {x}^{2} = 192 \times 3}$

$\displaystyle \sf{ \implies x = \pm \: \sqrt{ 192 \times 3}}$

$\displaystyle \sf{ \implies x = \pm \: \sqrt{ 64 \times 3\times 3}}$

$\displaystyle \sf{ \implies x = \pm \: (8 \times 3)}$

$\displaystyle \sf{ \implies x = \pm \: 24}$

FINAL ANSWER

Hence the required Geometric mean = - 24 or 24

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