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CBSE Class 10 Answered

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)
Asked by miniprasad | 08 Dec, 2018, 10:45: PM
answered-by-expert Expert Answer
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 begin mathsize 12px style a space equals space fraction numerator p squared plus q squared minus p minus q plus p q over denominator p q end fraction space space space a n d space space d space equals space minus fraction numerator 2 left parenthesis p plus q right parenthesis over denominator p q end fraction end style............................(3)
 
Sum of (p+q) terms  = begin mathsize 12px style open parentheses fraction numerator p plus q over denominator 2 end fraction close parentheses space open square brackets 2 a space plus space open parentheses p plus q minus 1 close parentheses d close square brackets end style..........................(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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