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Given an arithmetic series if the number of 8 first tribe 100 and the number 12 the first tribe 222 then the 6th tier of the series is ..... |
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Answer» // a = first term b = differences between tribes Un = tribe to n Sn = number of first n tribes // // search for 2a // Sn = n / 2 (2a + (n - 1) b S8 = 8/2 (2a + (8 - 1) b) (100) = 4 (2a + 7b) 8a = 100 - 28b // divided by 4 all // 2a = 25 - 7b // finds b by substituting 2a // S12 = n / 2 (2a + (n - 1) b) S12 = (12) / 2 ((25 - 7b) + (12 - 1) b) (222) = 6 (25 - 7b + 11b) 222/6 = 25 + 4b 4b = 37 - 25 b = 12/4 b = 3 // find a by substituting b // 2a = 25 - 7b 2a = 25 - 7 (3) 2a = 25 - 21 a = 4/2 a = 2 // searches for 6th / Un = a + (n - 1) b U6 = (2) + (6 - 1) (3) U6 = 2 + 5 (3) U6 = 2 + 15 U6 = 17 So the sixth row is 17 |
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