MathematicsState True/ False:If the pth, qth and rth term of an A.P. are a, b and c   respectively, then (a−b)r+(b−c)p+(c−a)q=0   and a(q−r)+b(r−p)+c(p−q)=0  .

State True/ False:


If the pth, qth and rth term of an A.P. are a, b and c   respectively, then (ab)r+(bc)p+(ca)q=0   and a(qr)+b(rp)+c(pq)=0  .


  1. A
    True
  2. B
    False  

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    Solution:

    Given that,
    The pth, qth and rth term of an A.P. are a, b and respectively.
    We are using the formula,
    l=a+(n1)d  
    Here, let’s assume A is the 1st term of the given A.P. and D is the common difference.
    Therefore, we have,
    a=A+(p-1)D
    b=A+(q-1)D
    c=A+(r-1)D
    We have,
    =(ab)r+(bc)p+(ca)q   Solving further,
    arbr+bpcp+cqaq   aqar (brbp)(cpcq)   a qr +b rp +c pq          0  Therefore, the statement is true.
    Hence, option 1 is correct.
     
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