10th Class Mathematics Solved Paper - Mathematics 2017 Delhi Set-III

  • question_answer If the \[{{p}^{th}}\] term of an A. P. is q and \[{{q}^{th}}\] term is p, prove that its \[{{n}^{th}}\] term is \[(p+q-n)\].


    Let a be first term and d be common difference.
    Then,                \[{{p}^{th}}\text{term}=q\Rightarrow a+(p-1)d=q\]                               ?(i)       
                            \[{{q}^{th}}\text{term}=p\Rightarrow a+(q-1)d=p\]                               ?(ii)
    On subtracting eq. (ii) from eq. (i)
         \[(p-q)d=q-p\] or \[d=\frac{q-p}{p-q}=-1\]
    Putting value of d in eq. (i)
                         \[{{T}_{n}}=q+p-n\]                               Hence Proved


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