Question

Howmany
terms of AP of the Al - 10-8,-6........ must be taken to give a sum of 0.​

Answer 1

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Step-by-step explanation:

Answer is in the attachment-:

Answer 2

GIVEN :-

• AP = -10 , -8 , -6 , ..........

TO FIND :-

• Number of terms must be taken to give a sum of 0 .

SOLUTION :-

     First term , a = -10

     Common difference , d  = -8 - (-10)

                                              = -8 + 10

                                              =  2

   

     $\bf Sum \ of \ first \ n \ terms \ of \ an \ AP =\dfrac{n}{2}\times (2a+(n-1)d)$

     Let there are n terms so that the sum is zero.

 

       $\longrightarrow\sf \dfrac{n}{2}\times (2a+(n-1)d)=0\\\\\longrightarrow \dfrac{n}{2} \times (2\times -10 +(n-1)\times 2)=0\\\\\longrightarrow -20 +(n-1)\times 2= 0\\\\\longrightarrow (n-1)\times 2 = 20 \\\\\longrightarrow (n-1) = 10 \\\\\longrightarrow n = 10+1 \\\\\longrightarrow \bf n = 11$

             

    11 terms of the sequence has to be taken so that their sum is zero.