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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.

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Given:

a9 = 19

a + 8d = 19 (i)

Acc. to question,

a19 = 3a6 (ii)

a19 = a + 18d

a= 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,.....

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