Q12 of 49 Page 1

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

The formula to find the nth term of an A.P. is given by,

an = a + (n – 1) d


⇒ a19 = a + 18d


⇒ a6 = a + 5d


⇒ a9 = a + 8d = 19 …. (i)


According to question,


a19 = 3 a6


⇒ a + 18d = 3 (a + 5d)


⇒ a + 18d = 3a + 15d


⇒ 2a = 3d


⸫ a = d


Substituting the value of a in eq (i), we get


⇒


⇒ 3d + 16d = 38


⸫ d = 2


⸫ a = 3


⸫ The terms of the A.P. are 3, 5, 7, 9, 11, …….nth


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