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Question

The number of terms common to the two arithmetic progressions
3,7,11,,407 and 2,9,16,,709 is 


Solution

Given A.P.s are 
3,7,11,,407 (common difference is 4)
2,9,16,,709 (common difference is 7)
We can observe that the first common term is 23.
( 6th term in 1st A.P. and 4th term in 2nd A.P. are same.)
Let the number of common terms be n.
They will be in A.P. with common difference =28 ( i.e., (LCM (4,7) )
Now, the last common term can't be greater than 407.
23+(n1)28407
n38428+1
n14.7n=14

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