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Question

If a1,a2,a3,... from a geometric progression and ai>0 for all i1, then ∣ ∣logamlogam+1logam+2logam+3logam+4logam+5logam+6logam+7logam+8∣ ∣ is equal to

A
logam+8logam
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B
logam
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C
2logam+1
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D
0
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Solution

The correct option is B 0
Since a1,a2,a3.... are in G.P
loga1,loga2,loga3,.... are in G.P
logam+logam+2=2logam+1
logam+3+logam+5=2logam+4
logam+6+logam+8=2logam+7
applying C2C2(1/2)(C1+C3) we get
Δ=∣ ∣logam0logam+2logam+30logam+5logam+60logam+8∣ ∣=0

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