If a,b,c∈R+ 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 c−a are in G.P.
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Solution
The correct option is Cc,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=bc⇒a2=(a+2c)c(From [1]) ∴c,a and a+2c are in G.P. a2=ac+2c2⇒a2−ac=2c2 So, a2,ac and c2 are not in A.P. a2(a−c)=c2 So, a2,c and c−a are not in G.P.