Maths **急 （請寫上步驟）

1. the n-th term of an arithmetic sequence is 2+5n .
Find the sum of the first 100 terms of the sequence.
The sequence is
2,7,12....
First term 2
difference 5
the sum of the first 100 terms
=n/2[2a+(n-1)d]
=100/2[2(2)+(100-1)(5)]
=50(499)
=24950
2. In a class, students study either History or Geography, but not both. If the number of students studying Geography is 50% more than those studying History, what is the percentage of students studying History?
Let there are total n students in a class
Let the number of students who study History is n(H)
Let the number of students who study Geography is n(G)
Then n(G)=1.5[n(H)]
But n(G)+n(H)=n
So 1.5[n(H)]+n(H)=n
2.5[n(H)]=n
n(H)/n=1/2.5=10/25=40%
So the percentage of students studying History is 40%


2007-04-18 02:14:53 補充：
第一題做錯了The sequence is 7,12,17....First term 7difference 5the sum of the first 100 terms=n/2[2a+(n-1)d] =100/2[2(7)+(100-1)(5)]=50(509)=25450不過下面個位第二條是做錯的。你代students=100便知道了

1.
因為a(n)=2+5n,n=100
a(1)=2+5*1=7,a(100)=2+5*100=502
S(100)
=[a(1)+a(100)]*100/2
=(7+502)*100/2
=25450
the sum of the first 100 terms of the sequence is 25450

2.
let x is the percentage of students studying History
即the number of students studying Geography is (x+50)%
(x+50)%+x%=100%
2x%=50%
x=25%
so 25% of students studying History

2007-04-18 23:53:21 補充：
sorry myisland8132說得對2.錯了,應是let x is the percentage of students studying History即the number of students studying Geography is x(1+50%)x(1+50%)+x=100%250%x=100%x=0.4so 40% of students studying History