Q. 394.7( 3 Votes )

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

Answer :

Given: a_{9} =19

a + 8d= 19 (i)

Acc. to question,

a_{19}= 3a_{6} (ii)

a_{19}=a + 18d

a_{6}=a + 5d

Putting the value of a_{19} and a_{6} 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

a_{1} = a=3

a_{2} =a +d=3 +2=5

a_{3} =a +2d=3 + 2(2)=7

Hence, the A.P. is

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