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Arithmetic Progression, Geometric Progression & Harmonic Progression

Posted January 9th, 2010 by alpha
in

If a,b,c are in A.P, b,c,d, are in G.P,c,d,e are in H.P. , then prove that a,c,e are in G.P.

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Comments

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answer

On January 9th, 2010 Structure says:
$$b=\frac{a+c}{2}$$
$$d=\frac{2ce}{c+e}$$
$$bd=c^2$$

but

$$bd=\frac{ce(a+c)}{c+e}=c^2$$

so

$$ae=c^2$$

I don't follow your last step.

On January 9th, 2010 alpha says:

-------------------x----------------------------
``Old theorems never die; they turn into definitions.''
----E. Hewitt

''ALPHA" =)

answer

On January 10th, 2010 Structure says:

Dear friend,

Take a pencil!

You must learn to fill the missing calculus.

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