JEE Main & Advanced Mathematics Sequence & Series Question Bank Self Evaluation Test - Sequences and Series

  • question_answer
    The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is

    A) 2

    B) 3

    C) \[\frac{3}{2}\]

    D) -1

    Correct Answer: A

    Solution :

    [a] Let the progression be a, \[a+d,a+2d,\] Then \[{{x}_{4}}=3{{x}_{1}}\Rightarrow a+3d=3a\Rightarrow 3d=2a\]   ... (i) Again  \[{{x}_{7}}=2{{x}_{3}}+1\] \[\Rightarrow \,\,a+6d=2(a+2d)+1\Rightarrow 2d=a+1\]      ... (ii) Solving (i) and (ii) we get \[a=3,\,\,d=2\]


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