InterviewSolution
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InterviewSolution
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Let `a_(1),a_(2),a_(3),a_(4)anda_(5)` be such that `a_(1),a_(2)anda_(3)` are in A.P., `a_(2),a_(3)anda_(4)` are in G.P., and `a_(3),a_(4)anda_(5)` are in H.P. Then, `a_(1),a_(3)anda_(5)` are inA. G.P.B. A.P.C. H.P.D. none of these |
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Answer» Correct Answer - A We have `a_(1),a_(2),a_(3)` are in A.P. `rArr2a_(2)=a_(1)+a_(3)` . . . .(i) `a_(2),a_(3),a_(4)` are in G.P. `rArr a_(3)^(2)=a_(2)a_(4)` . . .(ii) `a_(3),a_(4),a_(5)` are in G.P. `rArra_(4)=(2a_(3)a_(5))/(a_(3)+a_(5))` . . .(iii) Putting `a_(2)=(a_(1)+a_(3))/(2)anda_(4)=(2a_(3)a_(5))/(a_(3)+a_(5))` in (ii), we get `a_(3)^(2)=(a_(1)+a_(3))/(2)xx(2a_(3)a_(5))/(a_(3)+a_(5))` `rArr" "a_(3)^(2)=a_(1)a_(5)rArra_(1),a_(3),a_(5)` are in G.P. |
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