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Question

If bcad=b+ca+d=3(bcad), then a, b, c, d are in
  1. A.P
  2. G.P.
  3. H.P.
  4. A.GP


Solution

The correct option is C H.P.
bcad=b+ca+db+cbc=a+dbc1b+1c=1a+1d  ....(1)
bcad=3(bcad)adad=3(b+c)bc1d=1a+3(1c1b)      ....(2)
Let1b1a=α.Then (1)1d1c=α,
Substituting for1b1din(2),we get1c+α=1a+3c3(1a+α)
1c1a+2α.1b=1a+α,1c=1a+2α,1d=1a+3α1a,1b,1c,1d are in A.P. and f a, b, c, d are in H.P

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