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Find the middle term of the A.P. 6, 13, 20, ............. ,216 |
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Answer» The given AP is 6,13,20,........,216. First term, a = 6 Common difference, d = 13 - 6 = 7 Suppose these are n terms in the given AP. Then, an = 216 ⇒ 6 + (n - 1) × 7 = 216 [ an = a + (n-1) d] ⇒ 7(n - 1) = 216 - 6 = 210 ⇒ n - 1 = 210/7 = 30 ⇒ n = 30 + 1 = 31 Thus, the given AP contains 31 terms, ∴ Middle term of the given AP = (31 + 1/2)th term = 16th term = 6 + (16 - 1) × 7 = 6 + 105 = 111 Hence, the middle term of the given AP is 111. |
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