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10th Class Mathematics Arithmetic Progressions Question Bank Arithmetic Progressions

  • question_answer
    Find the sum of first 20 terms of an A.P. whose nth term is given by \[{{T}_{n}}=(7-3n).\];

    A) 382                 

    B)        \[-490\]           

    C) 420                 

    D)        \[-382\]           

    Correct Answer: B

    Solution :

    We have. \[{{T}_{n}}=(7-3n)\] First term, \[{{T}_{1}}=(7-3\times 1)=4\] Second term,  \[{{T}_{2}}=7-3\times 2=1\] Third term,  \[{{T}_{3}}=7-3\times 2=-2\] \[\therefore \]   Series is \[4,1,-2,\] .......... and common difference \[=-3\] Sum of first 20 terms \[({{S}_{20}})\] \[=\frac{20}{2}[2\times 4+(20-1)\,(-3)]=10\,[8-57]=-490\]


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