Question

3 geometric means between 3 and 1875

Answer 1

SOLUTION

TO DETERMINE

The 3 geometric means between 3 and 1875

EVALUATION

Let x, y, z be the 3 geometric means between 3 and 1875

Then 3, x, y, z, 1875 are in Geometric Progression

Here first term = a = 3

Let Common Ratio = r

Then

$\sf{}x = 3r$

$\sf{}y= 3 {r}^{2}$

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

$\sf{}1875 = 3 {r}^{4}$

Now

$\sf{}1875 = 3 {r}^{4} \: \: \: gives$

$\sf{}3 {r}^{4} = 1875$

$\implies\sf{} {r}^{4} =625$

$\implies \sf{} r = \pm \: 5 \: \: ( \because \: \: r \: is \: real)$

Taking r = 5

x = 15 , y = 75 , z = 375

Taking r = - 5

x = - 15 , y = 75 , z = - 375

FINAL ANSWER

Hence The 3 geometric means between 3 and 1875 are

15 , 75 , 375

or

- 15 , 75 , - 375

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LEARN MORE FROM BRAINLY

The G.M. of 3 and 24 with weight 2 and 1 respectively is

(A) 8 (B) 4 (C) 6 (D) 9

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