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Question

If a1,a2,a3,5,4,a6,a7,a8,a9 are H.P and D=∣ ∣a1a2a354a6a7a8a9∣ ∣, then the value of 21D.

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Solution

an=20n and d=120
∣ ∣a1a2a354a6a7a8a9∣ ∣
D=∣ ∣ ∣ ∣ ∣ ∣20202203204205206207208209∣ ∣ ∣ ∣ ∣ ∣
=(20)34×7∣ ∣ ∣ ∣ ∣ ∣112131452317879∣ ∣ ∣ ∣ ∣ ∣
Applying R1R1R2 and R2R2R3
=(20)34×7∣ ∣ ∣ ∣ ∣ ∣03101303401917879∣ ∣ ∣ ∣ ∣ ∣
=2034×7(3903120)
=2034×7(130140)
=2034×7(40301200)
=2034×7×1120
=20×20×204×7×1120
=5×107×13
=5021
21D=21×5021=50


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