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Question

If a, b,and c are in G.P. and x, y, respectively, be arithmetic means between a, b and b, c, then the value of ax+cyis


A

1

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B

2

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C

1/2

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D

none of these

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Solution

The correct option is B

2


Given, b2=ac and x=a+b2,y=b+c2.Therefore,

ax+cy=2aa+b+2cb+c

=2a(b+c)+2c(a+b)(a+b)(b+c)

=22ac+ab+bcab+ac+b2+bc

=22ac+ab+bc2ac+ab+bc

=2


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