# The 19th term of an AP is equal to 3 times its 6th term. If its 9th term is 19, find the AP.

Let a be the first term and d be the common difference.

Given: a9 = 19

a19 = 3 a6

Now, Consider a9 = 19

a + (9 - 1)d = 19

a + 8d = 19 ………………….(1)

Consider a19 = 3 a6

a + 18d = 3(a + 5d)

a + 18d = 3a + 15d

2a - 3d = 0 ………………….(2)

Now, subtracting twice of equation (1) from (2), we get,

- 19d = - 38

d = 2

from equation (1), we get,

a = 19 - 8d

a = 19 - 8 × 2

a = 19 - 16

a = 3

Thus the AP is a, a + d, a + 2d, a + 3d, a + 4d,….

Therefore the AP is 3, 5, 7, 9….

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