1.Given that (-1)^n is the general term of a sequence.Find the sum of
the first 2n terms.
2.The length of a rectangle is longer than twice the width by 1m. If
the perimeter is 26m, what is the length and width of the rectangle.
3.Peter and James have x marbles altogether.When Peter gives 4
marbles to James, then Peter has twice as many marbles as James.
When Peter gives 12 marbles to James ,then they have the same
number of marbles. Find the value of x.
F.1 maths(3 questions)
2008-12-27 5:05 pm
回答 (2)
2008-12-27 5:51 pm
✔ 最佳答案
1.Method 1:
(-1) + 1 + (-1) + 1 + (-1) + ....... 2nth term
Number of (-1) = n
Number of (1) = n
(-1) + 1 + (-1) + 1 + (-1) + ....... 2nth term
= n(-1) + n(1)
= -n + n
= 0
Method 2:
It is a geometric sequence.
First term a = (-1)1 = -1
Common ratio r = (-1)n+1/(-1)n = -1
Sum to 2n terms
= a(1 - r2n)/(1 - r)
= (-1)[1 - (-1)2n]/[1 - (-1)]
= 0
=====
2.
Let L m and W m be the length and the width respectively.
L - 2W = 1 ...... (1)
2(L + W) = 26 ...... (2)
(2):
L + W = 13 ...... (3)
(3) - (1):
3W = 12
W = 4
Put W = 4 into (3):
L + 4 = 13
L = 9
Ans: The length is 9 cm, and the width is 4 cm.
=====
3.
Let P and J be the numbers of marbles that Peter and James have respectively.
P - 4 = 2(J + 4) ...... (1)
P - 12 = J + 12 ...... (2)
(1):
P - 4 = 2J + 8
P - 2J = 12 ...... (3)
(2):
P - J = 24 ...... (4)
(4) - (3):
J = 12
Put J = 12 into (4):
P - (12) = 24
P = 36
x = P + J
x = 36 + 12
x = 48
=
2008-12-27 5:50 pm
1.the first term is -1
the 2nd term is 1
the 3rd term is -1
the 4th term is 1
.
.
the (2n-1)th term is -1 (as 2n must be a even number)
the (2n)th term is 1
The answer is 0.
2.Let the width be X.
so length is 2X+1.
2*(length + width)=26
2*(2X+1+X)=26
X=4
ANS:width is 4m & length is 9m
3.Let the amounts of James having be Y,
Peter having be Z .
Z - 4 = 2(Y + 4)......(1)
Z -12 = Y + 12........(2)
from(2) : Z = Y +24 ........(3)
put (3) into (1):
(Y + 24) - 4 = 2(Y + 4)
Y= 16
so Z= 40
ANS: x = 16 + 40 = 56
the 2nd term is 1
the 3rd term is -1
the 4th term is 1
.
.
the (2n-1)th term is -1 (as 2n must be a even number)
the (2n)th term is 1
The answer is 0.
2.Let the width be X.
so length is 2X+1.
2*(length + width)=26
2*(2X+1+X)=26
X=4
ANS:width is 4m & length is 9m
3.Let the amounts of James having be Y,
Peter having be Z .
Z - 4 = 2(Y + 4)......(1)
Z -12 = Y + 12........(2)
from(2) : Z = Y +24 ........(3)
put (3) into (1):
(Y + 24) - 4 = 2(Y + 4)
Y= 16
so Z= 40
ANS: x = 16 + 40 = 56
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