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C2 The 16th term of an AP is five times its third term. If its 10th term is 41, then find the sum ofits first fifteen terms. (495) |
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Answer» 16th term = a + 15d3rd term = a + 2d given 5(a + 2d) = a + 15d5a + 10d = a + 15d 4a - 5d = 0 4a = 5d a = 5d/4 Also, 10th term = a + 9d = 41 a = 5d/4 so, 5d/4 + 9d = 41 5d/4 + 36d/4 = 41 5d + 36d/4 = 41 41d/4 = 41 41d = 164 d = 164/41 d = 4 a + 9d = 41 a + 36 =41a = 5 --------------------------------------------- n = 15a = 5d = 4 Sn = n/2(2a + (n-1)d)= 15/2 (10 + 14 * 4)= 15/2*66 = 495 |
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