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Question

If first and (2n1)th terms of an A.P., G.P. and H.P. are equal and their nth terms are a, b, c respectively, then

A
a+c=2b
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B
abc
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C
a+c=b
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D
b2=ac
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Solution

The correct options are
B abc
D b2=ac
Given first and (2n1)th terms of AP,GP and HP are equal.

And nth terms are a,b and c respectively.

Let first and (2n1)th terms are x and y respectively.

a=x+y2

b=xy

c=2xyx+y

abc and b2=ac Since, AMGMHM and GM2=(AM)(HM)

Hence, options B and D.

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