10th Class Mathematics Solved Paper - Mathematics-2016 Delhi Term-II Set-II

  • question_answer How many terms of the A.P. 27, 24, 21,... should be taken so that their sum is zero?

    Answer:

    Given, A.P. is 27, 24, 21,...
    We have, \[a=27,\text{ }d=24-27=21-24=-3\]
    Now, \[{{S}_{n}}=0\]
    Therefore,                      \[{{S}_{n}}=\frac{n}{2}[2a+(n-1)d]=0\]
    \[\Rightarrow \,\frac{n}{2}[2(27)+(n-1)(-3)]=0\]
    \[\Rightarrow \,54-3n+3=0\]
    \[\Rightarrow \,57-3n=0\]
    \[\Rightarrow \,3n=57\]
    \[\therefore n=19\]
    Hence, the no. of terms are 19


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