Question

Insert 3 geometric means between 2 and 512.

Answer 1

SOLUTION

TO DETERMINE

Insert 3 geometric means between 2 and 512

EVALUATION

We have to Insert 3 geometric means between 2 and 512

Let x, y, z be the 3 geometric means between 2 and 512

Then 2 , x , y , z , 512 are in Geometric Progression

Let r be the Common Ratio

Then

x = 2r

$\sf{ y = 2 {r}^{2} \: }$

$\sf{ z = 2 {r}^{3} \: }$

$\sf{ 512= 2 {r}^{4} \: }$

So From the last equation

$\sf{ 2 {r}^{4} = 512\: }$

$\implies \sf{ {r} = \pm \: 4\: }$

Taking r = 4 the three Geometric means are

8 , 32 , 128

Taking r = - 4 the three Geometric means are

- 8 , 32 , - 128

FINAL ANSWER

The 3 geometric means between 2 and 512 are

8 , 32 , 128

OR

- 8 , 32 , - 128

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

The sum of the third and seventh term of an AP is 40 and the sum sixth and 14th terms is 70 .Find the sum of first ten terms

https://brainly.in/question/22811954