If x, 2y, 3z are in A.P., where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is
A
3
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B
13
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C
2
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D
12
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Solution
The correct option is B13 Since x, y, z are in G.P. Letx=a,y=ar,z=ar2,where'a'isthefirsttermandristhecommonratiooftheG.P.∴y2=xz
Also, x, 2y, 3z in A.P. 2(2y)=x+3z⇒4ar=a+3ar2⇒4r=1+3r2⇒3r2−4r+1=0⇒3r2−3r−r+1=0⇒3r(r−1)−1(r−1)=0⇒r=1(NotPossible as x, y, z are distinct)or13