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If a, b, c, d are four number such that first three are in AP and last three are in hp the1)bc=ad2)ac=bd3)ab=cd4lnone of this
2b= a+c....(i) c= 2bd/b+d.....(ii) Substituting the value of b from equation (i) to (ii) c =(2ad+2cd)/(a+c+2d) ac+c²+2cd = 2ad + 2cd ac+c² = 2ad c(a+c) = 2ad c (2b) = 2ad bc=ad. (Ans)
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