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10th Class Mathematics Arithmetic Progressions Question Bank Arithmetic Progressions

  • question_answer
    In an A.P., if the \[{{p}^{th}}\] term is 'q' and the \[{{q}^{th}}\] term is 'p', then its \[{{n}^{th}}\] term is _____.

    A) \[p+q-n\]        

    B) \[p+q+n\]      

    C)        \[p-q+n\]      

    D)        \[p-q-n\]          

    Correct Answer: A

    Solution :

    We have given that \[{{a}_{p}}=q\] and \[{{a}_{q}}=p\] \[\Rightarrow \]            \[q=a+(p-1)d\] and               ... (i) \[p=a+(q-1)d\]                     ... (ii) Subtracting (ii) from (i), we get       \[q-p=d(p-q)\Rightarrow d=-1\]           Now,  \[q=a+1-p\]                 [From (i)]; \[\Rightarrow \]            \[a=q+p-1\] \[\therefore \] \[{{a}_{n}}=a+(n-1)d=q+p-1+(n-1)(-1)\]             \[=q+p-1+1-n=q+p-n\]


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