# The 19th term of an A.P. is equal to three times its sixth term. If its 9th term is 19, find the A.P.

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

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