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KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    If A.M. between \[{{p}^{th}}\] and \[{{q}^{th}}\] terms of an A. P. be equal to the A.M. between \[{{r}^{th}}\] and \[{{s}^{th}}\] term of the A. P., then \[p+q\] is equal to

    A) \[r+s\]

    B) \[\frac{r-s}{r+s}\]

    C) \[\frac{r+s}{r-s}\]

    D) \[r+s+1\]

    Correct Answer: A

    Solution :

    \[\frac{{{t}_{P}}+{{t}_{q}}}{2}=\frac{{{t}_{r}}+{{t}_{s}}}{2}=a+(p-1)\,d+a+(q-1)\,d=\]\[a+(r-1)\,d+a+(s-1)\,d\]
    \[\therefore \]      \[p+q=r+s.\]


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