Question

Find two geometric mean between 1/4 and 2

Answer 1

Answer:

1/2,1

Step-by-step explanation:

a=1/4

4th term =2

ar^3 = 2

r^3 = 2*4

r^3=8

r=2

1/4,1/2 ,1,2 ....

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Answer 2

SOLUTION

TO DETERMINE

$\displaystyle \sf{ Two \: geometric \: mean \: between \: \: \frac{1}{4} \: and \: 2 }$

EVALUATION

Let x , y are two geometric mean between 1/4 and 2

Then 1/4 , x , y , 2 are in Geometric Progression

Let common ratio = r

Then we have

$\displaystyle \sf{ x = \frac{r}{4} }$

$\displaystyle \sf{ y = \frac{ {r}^{2} }{4} }$

$\displaystyle \sf{ 2= \frac{ {r}^{3} }{4} }$

Now

$\displaystyle \sf{ 2= \frac{ {r}^{3} }{4} }$

$\displaystyle \sf{ \implies \frac{ {r}^{3} }{4} = 2 }$

$\displaystyle \sf{ \implies {r}^{3} = 8 }$

$\displaystyle \sf{ \implies r = 2 }$

Thus we have

$\displaystyle \sf{ x = \frac{ {r}^{} }{4} = \frac{ {2}^{} }{4} = \frac{1}{2} }$

$\displaystyle \sf{ y = \frac{ {r}^{2} }{4} = \frac{ {2}^{2} }{4} = \frac{4}{4} = 1 }$

FINAL ANSWER

$\displaystyle \sf Two \: geometric \: mean \: between \: \frac{1}{4} \: and \: 2 \: are \ \: \frac{1}{2} \: and \: 1$

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