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AIEEE 2015 Sample Questions › Algebra questions › ap

if the sum f an A.P is same for p and q terms, show that the sum of p+q terms is 0........

S(p+q) >0 from graph ...how can it be 0 ?????
and if S(p+q)=0 wat is the other root

#Mathematics #Algebra

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qwerty ·Oct 30 '09 at 7:07

$S p = 2 p (2 a + [p - 1] d)$

$S q = 2 q (2 a + [q - 1] d)$

$S q = S p $

$q (2 a + [q - 1] d) = p (2 a + [p - 1] d)$

$2 a (q - p) = d (p 2 - p - (q 2 - q))$

$2 a (q - p) - d (p 2 - q 2 - (p - q)) = 0$

$2 a (q - p) - d ((p - q) (p + q) - (p - q)) = 0$

$2 a (q - p) + d ((q - p) (p + q) - (q - p)) = 0$

$2 a (p + q - 1) d = 0$

$ 2 (p + q) (2 a + (p + q - 1) d) = 0$ $= S p + q $

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∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

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