An A.P., a G.P. and a H.P. have the same firs | vedclass

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(b) Let $a$ and $b$ be the same first and last terms of the three progressions, each having $(2n + 1)$ terms.

Then the middle term of the $A.P.$ is

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$G.P.$

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(b) Let $a$ and $b$ be the same first and last terms of the three progressions, each having $(2n + 1)$ terms.

Then the middle term of the $A.P.$ is $\frac{{a + b}}{2}$.

The middle term of the $G.P.$ is $\sqrt {ab} $.

The middle term of the $H.P.$ is $\frac{{2ab}}{{a + b}}$.

Obviously, these terms are in $G.P.$

An $A.P.$, a $G.P.$ and a $H.P.$ have the same first and last terms and the same odd number of terms. The middle terms of the three series are in

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