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Activities - progressions problems (view source)
Revision as of 17:04, 12 August 2014
, 17:04, 12 August 2014→What is asked of student
#In this problem we prove that 'c' will be the harmonic mean between 'a' and 'b'
#In this problem we prove that 'c' will be the harmonic mean between 'a' and 'b'
#That is we just show that c = <math>\frac{2ab} {a + b}</math>
#That is we just show that c = <math>\frac{2ab} {a + b}</math>
==Solution of the problem==
Assumption :-
#He know the formula for A.M , G.M and H.M
#He know the basic operation.
#He know substitute the values
==Algorithm==
The formula for arithmetic mean between 'a' and 'b' is A.M = <math>\frac{a + b} {2}</math><br>
The formula for geometric mean between 'a' and 'b' is G.M = <math>\sqrt{ab}</math><br>
Then formula for harmonic mean between 'a' and 'c' is H.M = <math>\frac{2ab} {a + b}</math><br>
Let 'a' be the arithmetic mean of 'b' and 'c'<br>
That is a = <math>\frac{a + b} {2}</math><br>
Re-arrange the formula,<br>
2 = <math>\frac{b + c} {a}</math> --------->1<br>
Multiply both side by 'ab' we get,<br>
2ab = <math>\frac{ab(b + c)} {a}<br>
Also 'b' is the geometric mean between 'a' and 'c'<br>
That is b = <math>\sqrt{ac}</math><br>