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Question

If a, b, cR+ are such that 2a, b, 4c are in A.P. and c, a, and b are in G.P., then

A
a2, ac and c2 are in A.P.
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B
c, a and a+2c are in A.P.
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C
c, a and a+2c are in G.P.
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D
a2, c and ca are in G.P.
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Solution

The correct option is C c, a and a+2c are in G.P.
Since, 2a, b, 4c are in A.P.
b=a+2c....[1]
Also, c, a, and b are in G.P.
a2=bca2=(a+2c)c (From [1])
c, a and a+2c are in G.P.
a2=ac+2c2a2ac=2c2
So, a2, ac and c2 are not in A.P.
a2(ac)=c2
So, a2, c and ca are not in G.P.

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