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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? 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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