If $a, b, c$ are $pt h, qt h$ and $r t h$ terms respectively of an A.P prove that:
$p (b - c) + q (c - a) + r (a - b) = 0$

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a, b, c

are

pt h, qt h

and

r t h

terms respectively of an A.P prove that:

p (b - c) + q (c - a) + r (a - b) = 0

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Text solutionVerified

G i v e n, a, b, c a re t h e p^{t h}, q^{t h}, r^{t h} t er m s o f an A . P res p ec t i v e l y . ∴ (b - a) = (c - b) s am e co mm o n d i ff ere n ce . \Rightarrow (a - b) = (b - c) ⟶ (1) N o w, L H S = p (b - c) + q (c - a) + r (a - b) = a (b - c) + b (c - a) + c (a - b) (w e c an re pl a ce d p, q, r b y a, b, c a s a, b, c a re t h e p^{t h}, q^{t h}, r^{t h} t er m s o f an A . P res p ec t i v e l y) = ab - a c + b c - ba + c a - c b (s in ce ab = ba, b c = c b, c a = a c) = 0 = R H S He n ce, p (b - c) + q (c - a) + r (a - b) = 0 h e n ce p ro v e d .

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Question Text	If $a, b, c$ are $pt h, qt h$ and $r t h$ terms respectively of an A.P prove that: $p (b - c) + q (c - a) + r (a - b) = 0$
Answer Type	Text solution:1
Upvotes	150