Q. 394.1( 13 Votes )

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

Answer :

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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