標題:
F.6 Maths A.S.
發問:
The product of the first term and the 6th term of an arithmetic sequence is -38. The sum of the 3rd term and the 4th term is 17. If the first term is positive, find the first term and the common difference of the sequence.
同學你好~ Let a be the first term and d be the common difference of the sequence. It is given that (1) a * (a+5d) = -38 (2) (a+2d) + (a+3d) = 17 (3) a > 0 From (2), 2a+5d=17 => 5d = 17-2a Put into (1), a * (a+17-2a) = -38 a * (17-a) = -38 17a - a2 = -38 a2 - 17a - 38 = 0 (a-19)(a+2)=0 a = 19 or -2 (rejected by (3)) Therefore, a = 19. d = (17-2a)/5 = (17-38)/5 = -21/5 = -4.2.
其他解答:
F.6 Maths A.S.
發問:
The product of the first term and the 6th term of an arithmetic sequence is -38. The sum of the 3rd term and the 4th term is 17. If the first term is positive, find the first term and the common difference of the sequence.
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最佳解答:同學你好~ Let a be the first term and d be the common difference of the sequence. It is given that (1) a * (a+5d) = -38 (2) (a+2d) + (a+3d) = 17 (3) a > 0 From (2), 2a+5d=17 => 5d = 17-2a Put into (1), a * (a+17-2a) = -38 a * (17-a) = -38 17a - a2 = -38 a2 - 17a - 38 = 0 (a-19)(a+2)=0 a = 19 or -2 (rejected by (3)) Therefore, a = 19. d = (17-2a)/5 = (17-38)/5 = -21/5 = -4.2.
其他解答:
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