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Page 255 Question 7 The sum of p terms of an AP is q and sum of q terms is p. Then prove that the sum of (p+q) terms is –(p+q)
Let a be the first term and d be the common difference

Sum of p terms = (p/2) [2a +(p-1)d ]= q   or 2a +(p-1)d = 2q/p ...................(1)
Sum of q terms = (q/2)[ 2a + (q-1)d]= p   or 2a +(q-1)d = 2p/q ....................(2)

Eqns.(1) and (2) are two linear equations. These equations can be solved to get a and d

we get ............................(3)

Sum of (p+q) terms  = ..........................(4)
substitute for a and d using eqn.(3) in eqn.(4) and simplify the algebric expression to get the answere -(p+q)
Answered by Thiyagarajan K | 09 Dec, 2018, 09:13: PM

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