Question

Find 10 arithmetic Mean, Geometric Mean and harmonic Mean between 50 and 100

Answer 1

Given : 50 and 100 ​

To Find :  10 arithmetic mean and  10  geometric mean between  50 and 100 ​

Solution:

50 and 100 ​

10 arithmetic mean

Then total terms = 12

a = 50

12th term = 100

100 = 50 + (12- 1)d

=> d = 50/11

10 arithmetic means

50 + 50/11  , 50 + 2*50/11 , _____ , 50 + 9*50/11 , 50 + 10 *50/11

600/11 , 650/11 , 700/11 , 750/11 , 800/11 , 850/11 , 900/11 . 950/11 , 1000/11 , 1050/11

10 geometric mean

Then total terms = 12

a = 50

12th term = 100

100 = 50r¹¹

=> r¹¹ = 2

=> $r=\sqrt[11]{2}$

10 geometric mean

50$\sqrt[11]{2}$    , 50$\sqrt[11]{2^2}$ ,   50$\sqrt[11]{2^3}$    , 50$\sqrt[11]{2^4}$ ,    50$\sqrt[11]{2^5}$    , 50$\sqrt[11]{2^6}$ ,  50$\sqrt[11]{2^7}$    , 50$\sqrt[11]{2^8}$ ,  50$\sqrt[11]{2^9}$    , 50$\sqrt[11]{2^{10}}$

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