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  4. If the first and the (2n+1)th terms of an A.P., G.P. and H.P. are equal and their nth terms are respectively a, b, c then always

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Q. If the first and the $(2n+1)^{th}$ terms of an $A.P., G.P.$ and $H.P.$ are equal and their $n^{th}$ terms are respectively $a, b, c$ then always

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Solution:

There seems to be a printing mistake here
If there are $(2n-1)$ terms instead of $(2n + 1)$ terms then $n^{th}$ terms of the A.P., G.P. and H.P. are the A.M., G.M. & H.M of the first and the last terms.
So, $a\ge b\ge c\, \&\, ac-b^{2}\left(B, D\right)$
otherwise if there are $(2n + 1)$ terms then the $n^{th}$ terms should be in decreasing order of $A.P., G.P$. & $H.P.$
i. e.$a\ge b\ge c \left(B\right)$