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JEE Main & Advanced Mathematics Sequence & Series Question Bank Arithmetic Progression

  • question_answer
    Let \[{{S}_{n}}\]denotes the sum of \[n\] terms of an A.P. If \[{{S}_{2n}}=3{{S}_{n}}\], then ratio \[\frac{{{S}_{3n}}}{{{S}_{n}}}=\]   [MNR 1993; UPSEAT 2001]

    A) 4

    B) 6

    C) 8

    D) 10

    Correct Answer: B

    Solution :

    \[{{S}_{2n}}=3{{S}_{n}}\] \[\Rightarrow \]\[\frac{2n}{2}\{2a+(2n-1)d\}=3\ .\ \frac{n}{2}\{2a+(n-1)d\}\] \[\Rightarrow \]\[2a=(n+1)d\] Put \[2a=(n+1)d\] in\[\frac{{{S}_{3n}}}{{{S}_{n}}}\], we get its value 6.


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