Given:
a9 = 19
a + 8d = 19 (i)
Acc. to question,
a19 = 3a6 (ii)
a19 = a + 18d
a6 = a + 5d
Putting the value of a19 and a6 in (ii)
a + 18d = 3(a +5d)
3d = 2a
3d = 2(19 - 8d) (from (i))
19d = 38
d = 2
Now, putting the value of d in (i)
a = 19 - 8(2) = 3
a1 = a = 3
a2 = a +d = 3 +2 = 5
a3 = a +2d = 3 + 2(2) = 7
Hence, the A.P. is 3, 5, 7, 9,.....