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If pth, qth and rth terms of an A.P. are...

If pth, qth and rth terms of an A.P. are a,b,c, respectively, then show that
(i) a(q-r)+b(r-p)+c(p-q)=0
(ii) (a-b)r+(b-c)p+(c-a)q=0

Text Solution

AI Generated Solution

To solve the problem, we need to prove two statements based on the given terms of an arithmetic progression (A.P.). Let's denote the first term of the A.P. as \( a \) and the common difference as \( d \). ### Given: - The \( p \)-th term is \( a \) - The \( q \)-th term is \( b \) - The \( r \)-th term is \( c \) ### Step 1: Express the terms in terms of \( a \) and \( d \) ...
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Knowledge Check

  • If the pth, qth and rth terms of an A.P. are a,b,c respectively , then the value of a(q-r) + b(r-p) + c(p-q) is :

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    C
    p + q + r
    D
    pqr

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