a,b,c,d are in increasing GP. AM between a and b is 6. AM between c and d is 54. Then AM between a and d is:
(A)15 (B)48 (C)44 (D)42

Let α be the first term and r be common ration of the given G.PGiven a,b,c,d are in increasing G.Pi.e., α,αr,αr2,αr3  are in increasing G.Pand a+b2=6    α+αr2=6α(1+r)=12    ...(1)and c+d2=54αr2+αr32=54αr2(1+r)=108r2×12=108   [using 1]r2=9r=±3When r=3 then (1) becomesα(1+3)=12α=3When r=-3 then (1) becomesα(1-3)=12α=-6So, A.M between a and d=a+d2=α+αr32=3+3332 or -6+(-6)-332=42 or 78Please recheck your options.

  • 7
In the soln.u can also take value of a as -6 but it wll not give the required ans available in options.so a=3 for options.

  • 1
What are you looking for?