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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?

Grade:12

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
10 years ago
For first AP,
An = 2 + (x-1)3 = 3x - 1 where 0<x<51
For second AP,
Bn = 3 + (y-1)2 = 2y + 1 where 0<y<61
Now, for An = Bn
3x-1 = 2y + 1
3x - 2y = 2
where x and y are integers.
When x is an even no. , it satisfies this condition. Hence,
x=2, y = 2
x=4, y = 5
x=6, y = 8
.
.
.
.
x =40 , y= 59
Hence, 20 terms are identical.
Thanks
Bharat Bajaj
askiitians faculty
IIT Delhi

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