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

Options

A. `a=b=c`
B. `a+c=b`
C. `agt bgt c`
D. `ac-b^2=0`

Answer

C, D

Explanation

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`