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

  • question_answer
    If \[p\]times the \[{{p}^{th}}\] term of an A.P. is equal to \[q\] times the \[{{q}^{th}}\] term of an A.P., then \[{{(p+q)}^{th}}\] term is [MP PET 1997; Karnataka CET 2002]

    A) 0

    B) 1

    C) 2

    D) 3

    Correct Answer: A

    Solution :

    \[p\{a+(p-1)\,d\}=q\{a+(q-1)\,d\}\] \[\Rightarrow \] \[a(p-q)+({{p}^{2}}-{{q}^{2}})\,d+(q-p)\,d=0\] \[\Rightarrow \] \[(p-q)\{a+(p+q-1)\,d\}=0\] \[\Rightarrow \] \[a+(p+q-1)\,d=0\]\[\Rightarrow \]\[{{T}_{p+q}}=0\], \[\{\because \ p\ne q\}\].


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