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

  • question_answer
    If \[{{S}_{n}}=nP+\frac{1}{2}n(n-1)Q\], where \[{{S}_{n}}\] denotes the sum of the first \[n\] terms of an A.P., then the common difference is [WB JEE 1994]

    A) \[P+Q\]

    B) \[2P+3Q\]

    C) \[2Q\]

    D) \[Q\]

    Correct Answer: D

    Solution :

    Obviously\[{{S}_{n}}=\frac{n}{2}\{2P+(n-1)Q\}\], hence\[d=Q\]. Aliter: \[d={{T}_{2}}-{{T}_{1}}\]\[=({{S}_{2}}-{{S}_{1}})-{{S}_{1}}\]                   \[={{S}_{2}}-2{{S}_{1}}=2P+Q-2P=Q.\]


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