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The sum of 5th and 9th terms of an A.P is 30. If its 25th term is thrice its 8th term.find A.p |
| Answer» The sum of 5th and 9th term is 30.⇒ a + 4d + a + 8d = 30⇒ 2a + 12d = 30 ..................(1)And,Its 25th term is 3 times its 8th term.⇒ a + 24d = 3(a + 7d)⇒ a + 24d = 3a + 21d⇒ a + 24d - 3a - 21d = 0⇒ - 2a + 3d = 0 ...................(2)Adding equation (1) and (2).⇒ 2a +12d = 30\xa0 - 2a + 3d = 0________________ 15d = 30________________⇒ 15d = 30⇒ d = 30/15⇒ d = 2So, common difference, \'d\' is 2.Putting the value of d = 2 in the equation (1).2a + 12d = 30⇒ 2a + (12*2) = 30⇒ 2a = 24 = 30⇒ 2a = 30 - 24⇒ 2a = 6⇒ a = 6/2⇒ a = 3So, the first term of the required AP is 3So, the required AP is 3, 5, 7, 9, 11, 13, 15, 19,............. | |