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In an A.P 2,5,8....., upto 50 terms,and 3,5,7,9,... upto 60 terms,find how many terms are identical?
For first AP,An = 2 + (x-1)3 = 3x - 1 where 0<x<51For second AP,Bn = 3 + (y-1)2 = 2y + 1 where 0<y<61Now, for An = Bn3x-1 = 2y + 13x - 2y = 2where x and y are integers.When x is an even no. , it satisfies this condition. Hence,x=2, y = 2x=4, y = 5x=6, y = 8....x =40 , y= 59Hence, 20 terms are identical.ThanksBharat Bajajaskiitians facultyIIT Delhi
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