1. The sum of the first three terms of an arithmetic series (A.P.) is 48 and the fifth term is 37.
a) Find the first terms and the common difference of the series.
b) Use your answer to (a) to calculate the sum of the firsst twenty terms of the series.
2)Find the sum of the infinite geometic series (G.P.) which has first term 6 and common ratio -1/2 (negative one over two)
想問你地呢條maths .. plz help 15 points
2006-10-31 4:44 am
回答 (3)
2006-10-31 4:52 am
✔ 最佳答案
1. Let a and d be the first term and the common difference respectively.(a) a + a + d + a + 2d = 48...........(1)
a + 4d = 37...............................(2)
From (1), 3a + 3d = 48
a + d = 16
a = 16 - d..................................(3)
Sub (3) into (2), 16 - d + 4d = 37
3d = 21
d = 7. Thus a = 16 - 7 = 9
The first term is 9. The common difference is 7.
(b) Sum of the first 20 terms
= (20 / 2)[2 * 9 + (20 - 1) * 7]
= 10[18 + 133]
= 1510
2. Sum to infinity
= a / (1 - r)
= 6 / (1 - (-1 / 2))
= 6 / (3 / 2)
= 6 * 2 / 3 = 4
2006-11-03 7:22 pm
1. Let a and d be the first term and the common difference respectively.
(a) a + a + d + a + 2d = 48...........(1)
a + 4d = 37...............................(2)
From (1), 3a + 3d = 48
a + d = 16...........................(3)
(2)-(3): 3d = 21
d = 7.
Put d = 7 into (3)
Thus a = 16 - 7 = 9
The first term is 9. The common difference is 7.
(b) AP sum: n/2[2n+(n-1)d]
thus, sum of the first 20 terms
= (20 / 2)[2 * 20 + (20 - 1) * 7]
= 10[40 + 133]
= 1730
2. Sum to infinity
= a / (1 - r)
= 6 / (1 - (-1 / 2))
= 6 / (3 / 2)
= 6 * 2 / 3 = 4
(a) a + a + d + a + 2d = 48...........(1)
a + 4d = 37...............................(2)
From (1), 3a + 3d = 48
a + d = 16...........................(3)
(2)-(3): 3d = 21
d = 7.
Put d = 7 into (3)
Thus a = 16 - 7 = 9
The first term is 9. The common difference is 7.
(b) AP sum: n/2[2n+(n-1)d]
thus, sum of the first 20 terms
= (20 / 2)[2 * 20 + (20 - 1) * 7]
= 10[40 + 133]
= 1730
2. Sum to infinity
= a / (1 - r)
= 6 / (1 - (-1 / 2))
= 6 / (3 / 2)
= 6 * 2 / 3 = 4
參考: my knowledge (I am a F.5 tutor in a famous sec. school)
2006-10-31 4:58 am
(a) The general form of an arithmetic series (A.P) is
a, a+d, a+2d, a+3d, a+4d, + .....................
The sum of the first three terms is 48
i.e. a+(a+d)+(a+2d) = 48 ................equation (i)
The fifth term is 37
i.e. a+4d = 37 .............................equation (ii)
Solve both the equation (i) and (ii) , it can find the value of a and d.
a, a+d, a+2d, a+3d, a+4d, + .....................
The sum of the first three terms is 48
i.e. a+(a+d)+(a+2d) = 48 ................equation (i)
The fifth term is 37
i.e. a+4d = 37 .............................equation (ii)
Solve both the equation (i) and (ii) , it can find the value of a and d.
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