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  4. If an be the nth term of an AP and if a7=15, then the value of the common difference that would make a2a7a12 greatest is

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Q. If $ {{a}_{n}} $ be the nth term of an AP and if $ {{a}_{7}}=15, $ then the value of the common difference that would make $ {{a}_{2}}{{a}_{7}}{{a}_{12}} $ greatest is

JamiaJamia 2010

Solution:

Let d be the common difference of AP. Since, $ {{a}_{7}}=15 $ $ \therefore $ $ {{a}_{2}}=15-5d $ and $ {{a}_{12}}=15+5d $ Now, $ {{a}_{2}}{{a}_{7}}{{a}_{12}}=(15-5d)(15)(15+5d) $ $ =15.25(3-d)(3+d) $ $ =375(9-{{d}^{2}}) $ Clearly, this will be greatest, if $ d=0 $