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h v Grade: 12
        

The 10th common term between the series 3+7+11+.......  and 1+6+11+......... is


a)191


b)193


c)211


d)none of these

7 years ago

Answers : (2)

AskIITians Expert Hari Shankar IITD
17 Points
										

Any term of the first series can be written as 3+4(n-1) = 4n-1


Any term of the second series can be written as 1+5(m-1) = 5m-4


Here, m and n are natural numbers.


For commen term, 4n-1 = 5m-4


or 4n = 5m - 3...............(1)


Try putting m=1,2,3... and calculate n each time.


eg. for m=1, 4n = 2, or n = 1/2. But 1/2 is not a natural number.


So try m=2, 4n = 10-3= 7. not a natural number


For m=3, 4n = 15-3 = 12. or n = 3.


So, condition (1) is first satisfied by n = 3.


Obviously, since the LCM of 4 and 5 is 20, the next time it will be satisfied is when 5m-3 = 20+12.


Basically, it will be satisfied whenever 5m-3 = 20k+12, where k is a WHOLE number.


This gives n = (5m-3)/4 = 5k+3.


So, the common terms are 4n-1 = 4(5k+3)-1 = 20k+11


eg. the first sommon term is 11, when k=0. The second common term is 31, when k=1 and so on.


So the 10th common term will be 20(9)+11 = 191


 


A Shortcut


In all such questions, the nth common term is given by (LCM of common differences)*(n-1) + first common term


In this particular question, common differences of the 2 series are 4 and 5. Their LCM is 20. And the first common term is 11.


So the 10th common term is 20(10-1)+11 = 191.


This way you can also do questions where you have to find common terms of 3 or more series.

7 years ago
h v
33 Points
										

thanks for the answer

6 years ago
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