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The corresponding first and the (2n-1)th...

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

A

`a=b=c`

B

`a+c=b`

C

`agt bgt c`

D

`ac-b^2=0`

Text Solution

Verified by Experts

The correct Answer is:
C, D
Cosider the A.P since a is equidistant from the first term `alpha` and the last term `beta` of the A.P., therefore `alpha, a beta` are in A.P.
Hence a is the A.M. of `alpha` and `beta`. So,
`a = (alpha + beta)/(2)`
Similarly, b and c are the geometric and hormoic means, i.e.,
`b = sqrt(alpha beta)` and `c = (2 alpha beta)/(alpha + beta)`
Since A.M., G.M., and H.M. are in G.P and A.M `ge` G.M `ge` H.M., therefore a,b,c, are in G.P and `a ge b ge c`
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