Q. 394.7( 6 Votes )

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.

Answer :

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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