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Grade: 12

                        

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?

6 years ago

Answers : (1)

bharat bajaj
IIT Delhi
askIITians Faculty
122 Points
							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
6 years ago
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