Answer :

The formula to find the nth term of an A.P. is given by,

an = a + (n – 1) d


a19 = a + 18d


a6 = a + 5d


a9 = a + 8d = 19 …. (i)


According to question,


a19 = 3 a6


a + 18d = 3 (a + 5d)


a + 18d = 3a + 15d


2a = 3d


a = d


Substituting the value of a in eq (i), we get



3d + 16d = 38


d = 2


a = 3


The terms of the A.P. are 3, 5, 7, 9, 11, …….nth


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