InterviewSolution
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InterviewSolution
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Find the second term and nth term of an A.P. whose 6th term is 12 and 8th term is 22. |
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Answer» Given : 6th term of an A.P is 12 and 8th terms of an A.P. is 22 ⇒ a6 = 12 and a8 = 22 We know, an = a + (n – 1)d where a is first term or a1 and d is common difference and n is any natural number When n = 6 : ∴ a6 = a + (6 – 1)d ⇒ a6 = a + 5d Similarly, When n = 8 : ∴ a8 = a + (8 – 1)d ⇒ a8 = a + 7d According to question : a6 = 12 and a8 = 22 ⇒ a + 5d = 12 ………………(i) And a + 7d = 22…………..(ii) Subtracting equation (i) from (ii) : a + 7d – (a + 5d) = 22 – 12 ⇒ a + 7d – a – 5d = 10 ⇒ 2d = 10 ⇒ d = \(\frac{10}{2}\) ⇒ d = 5 Put the value of d in equation (i) : a + 5(5) = 12 ⇒ a + 25 = 12 ⇒ a = 12 – 25 ⇒ a = -13 As, an = a + (n – 1)d a2 = a + (2 – 1)d ⇒ a2 = a + d Now, Put the value of a = 9 and d = 2 in an and a2 ⇒ an = a + (n – 1)d ⇒ an = -13 + (n – 1)5 ⇒ an = -13 + 5n – 5 ⇒ an = -18 + 5n a2 = a + d ⇒ a2 = -13 + 5 ⇒ a2 = -8 Hence, 2th term and nth of the given A.P. are -8 and 5n – 18 respectively. |
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