標題:
發問:
1 ) consider an arithmetic sequence with the fourth term is 53 and the second term is three times the 21 st term . a)find the first erm and the common difference.b)find the sum of the first 21 terms of the arithmetic sequence 2 )the sum of the first n terms of an arithmetic sequence is n^2 +6n. find the... 顯示更多 1 ) consider an arithmetic sequence with the fourth term is 53 and the second term is three times the 21 st term . a)find the first erm and the common difference. b)find the sum of the first 21 terms of the arithmetic sequence 2 )the sum of the first n terms of an arithmetic sequence is n^2 +6n. find the nth term of the sequence. 需要清晰計算步驟
最佳解答:
1 ) Consideran arithmetic sequence with the fourth term is 53 and the second term is threetimes the 21st term . a) Find the first Term and the commondifference. b) Find the sum of the first 21terms of the arithmetic sequence Solution : a) First term, T(1) = a Common difference = d T(4) = 53 a + 3d = 53 a = 53 - 3d ...... [1] T(2) = 3T(21) a + d = 3(a + 20d) a + d = 3a + 60d 2a + 59d = 0 ...... [2] Put [1] into [2] : 2(53 - 3d) + 59d = 0 106 - 6d + 59d = 0 53d = -106 d = -2 Put d = -2 into [1] : a = 53 - 3*(-2) a = 59 Hence, the first term is 59 and the common difference is -2. b) Sum of the first 21st term = n[2a + (n - 1)d/2 = 21[2*59 + 20*(-2)]/2 = 819 2 ) The sum of the first n termsof an arithmetic sequence is n2 + 6n. find the nth term of the sequence. Solution : First term, T(1) = a Common difference = d S(n) = n2 + 6n n[2a + (n - 1)d]/2 = n2 + 6n 2a + (n - 1)d = 2n + 12 2a + nd - d = 2n + 12 dn + (2a - d) = 2n + 12 Compare the both sides: d = 2 and 2a - d = 12 d = 2 and 2a - 2 = 14 d = 2 and a = 7 The nth term = a + (n - 1)d = 7 + (n - 1)*2 = 7 + 2n - 2 = 2n + 5
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Arithmetic sequence問題 急!!!發問:
1 ) consider an arithmetic sequence with the fourth term is 53 and the second term is three times the 21 st term . a)find the first erm and the common difference.b)find the sum of the first 21 terms of the arithmetic sequence 2 )the sum of the first n terms of an arithmetic sequence is n^2 +6n. find the... 顯示更多 1 ) consider an arithmetic sequence with the fourth term is 53 and the second term is three times the 21 st term . a)find the first erm and the common difference. b)find the sum of the first 21 terms of the arithmetic sequence 2 )the sum of the first n terms of an arithmetic sequence is n^2 +6n. find the nth term of the sequence. 需要清晰計算步驟
最佳解答:
1 ) Consideran arithmetic sequence with the fourth term is 53 and the second term is threetimes the 21st term . a) Find the first Term and the commondifference. b) Find the sum of the first 21terms of the arithmetic sequence Solution : a) First term, T(1) = a Common difference = d T(4) = 53 a + 3d = 53 a = 53 - 3d ...... [1] T(2) = 3T(21) a + d = 3(a + 20d) a + d = 3a + 60d 2a + 59d = 0 ...... [2] Put [1] into [2] : 2(53 - 3d) + 59d = 0 106 - 6d + 59d = 0 53d = -106 d = -2 Put d = -2 into [1] : a = 53 - 3*(-2) a = 59 Hence, the first term is 59 and the common difference is -2. b) Sum of the first 21st term = n[2a + (n - 1)d/2 = 21[2*59 + 20*(-2)]/2 = 819 2 ) The sum of the first n termsof an arithmetic sequence is n2 + 6n. find the nth term of the sequence. Solution : First term, T(1) = a Common difference = d S(n) = n2 + 6n n[2a + (n - 1)d]/2 = n2 + 6n 2a + (n - 1)d = 2n + 12 2a + nd - d = 2n + 12 dn + (2a - d) = 2n + 12 Compare the both sides: d = 2 and 2a - d = 12 d = 2 and 2a - 2 = 14 d = 2 and a = 7 The nth term = a + (n - 1)d = 7 + (n - 1)*2 = 7 + 2n - 2 = 2n + 5
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