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