Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

Let first term be a and common difference be d. By formula, a n = a + (n - 1)d Given, ⇒ a 11 = 38 ⇒ a + (11 - 1)d = 38 ⇒ a + 10d = 38 .......(1) Given, ⇒ a 16 = 73 ⇒ a + (16 - 1)d = 73 ⇒ a + 15d = 73 ........(2) Subtracting equation (1) from (2), we get : ⇒ a + 15d - (a + 10d) = 73 - 38 ⇒ a - a + 15d - 10d = 35 ⇒ 5d = 35 ⇒ d = ⇒ d = 7. Substituting value of d in equation (1), we get : ⇒ a + 10 × 7 = 38 ⇒ a + 70 = 38 ⇒ a = 38 - 70 = -32. 31st term = a 31 = a + (31 - 1)d = -32 + 30 × 7 = -32 + 210 = 178. Hence, 31st term of A.P. = 178.

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Mathematics

Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

AP

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Check whether -150 is a term of the AP : 11, 8, 5, 2 …….

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