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+1 vote
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in Geometric Progressions by (15.7k points)

Find the GM between the numbers 

(i) 5 and 125 

(ii) 1 and \(\frac{9}{16}\)

(iii) 0.15 and 0.0015 

(iv) -8 and -2 

(v) -6.3 and -2.8 

(vi) ad ab3

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1 Answer

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(i) 5 and 125 

To find: Geometric Mean 

Given: The numbers are 5 and 125 

Formula used: 

(i) Geometric mean between a and b = \(\sqrt{ab}\)

Geometric mean of two numbers = \(\sqrt{ab}\)

\(\sqrt{5 \times 25}\)

\(\sqrt{625}\)

= 25 

The geometric mean between 5 and 125 is 25

(ii) 1 and \(\frac{9}{16}\)

To find: Geometric Mean

Given: The numbers are 1 and \(\frac{9}{16}\)

Formula used: (i) Geometric mean between a and b = \(\sqrt{ab}\)

Geometric mean of two numbers = \(\sqrt{ab}\)

The geometric mean between 1 and \(\frac{9}{16}\) is \(\frac{3}{4}\)

(iii) 0.15 and 0.0015 

To find: Geometric Mean

Given: The numbers are 0.15 and 0.0015 

Formula used: (i) Geometric mean between a and b = \(\sqrt{ab}\)

Geometric mean of two numbers = \(\sqrt{ab}\)

= 0.015 

The geometric mean between 0.15 and 0.0015 is 0.015. 

(iv) -8 and -2 

To find: Geometric Mean 

Given: The numbers are -8 and -2 

Formula used: (i) Geometric mean between a and b = \(\sqrt{ab}\)

Geometric mean of two numbers  = \(\sqrt{ab}\)

Mean is a number which has to fall between two numbers. 

Therefore we will take -4 as our answer as +4 doesn’t lie between -8 and -2 

The geometric mean between -8 and -2 is -4. 

(v) -6.3 and -2.8 

To find: Geometric Mean

Given: The numbers are -6.3 and -2.8 Formula used: 

(i) Geometric mean between a and b = \(\sqrt{ab}\)

Geometric mean of two numbers = \(\sqrt{ab}\)

Mean is a number which has to fall between two numbers. 

Therefore we will take -4.2 as our answer as +4.2 doesn’t lie between -6.3 and -2.8 

The geometric mean between -6.3 and -2.8 is -4.2. 

(vi) a3b and ab3 

To find: Geometric Mean Given: 

The numbers are ab and ab3 

Formula used: 

(i) Geometric mean between  a and b = \(\sqrt{ab}\)

Geometric mean of two numbers  = \(\sqrt{ab}\)

The geometric mean between a3b and ab3 is a2b2

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