If Sr denotes the sum of r terms of an A.P. and Sa/a2 = Sb/b2 = c . Then Sc is

(A) c3 (B) c/ab (C) abc (D) a+b+c . Give the process also .

Ans. (A)
Solution: 
Sum of r terms in an AP is given by : Sr=r22A+(r-1)Dwhere A = first termand D= common differenceGiven that: Saa2=ca22A+(a-1)Da2=c2A+(a-1)D2a=c2A+(a-1)D=2ac    (i)Similarly, for  Sbb2=c, 2A+(b-1)D=2bc    (ii)Solvig eq.s (i) and (ii) for A and D, we get:A=c and D=2cNow, Sc=c22A+(c-1)D=c22c+(c-1)2c=c2x2cx1+c-1=c3

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