Question

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Answer 1

Answer:

Step-by-step explanation:

Let a1 be the first term of AP and d be the common difference We know that nth term of AP is given by  an = a1 + (n-1) dGiven pth , qth and rth terms are a , b and c respectively  ap = a1 + (p – 1) d       = a1+ (pd – d) = a  → (1) aq = a1 + (q – 1) d         = a1 + (qd – d) = b → (2) ar = a1 + (r – 1) d       =  a1 + (rd – d) = c  → (3) Subtract (3) from (2), we get  (b - c)  = ( q -r) d  Hence (q – r) = (b – c) /d   → (4) Subtract (1) from (3), we get (c – a)  = (r – p) d  Hence (r – p) = (c – a)/d   → (5) Subtract (2) from (1), we get (a - b)  = (p – q) d  Hence (p – q) = (a – b)/d   → (6)  Consider the LHS : a(q – r) + b(r – p) + c(p – q)   a (q – r) + b (r – p) + c(p – q) Substitute the above values from (4), (5) and )6) we get  a (q – r) + b (r – p) + c(p – q) = 0 = RHS

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Answer 2

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