1) In a geometric sequence, the sum of the 1st term and the 3rd term is 250, and the sum of the 3rd term and the 5th term is 2250.
(a) Find the common ratio of the geometric sequence.
(b) Find the 1st term of the geometric sequence.
2) Consider four numbers 27, x, y, 6.
(a) Given that the first three numbers form a geometric sequence, express y in terms of x.
(b) Given that the last three numbers form a arithmetic sequence, express y in terms of x.
這兩題怎樣做? thx ^^
F.5 MATHS兩題
2007-10-08 6:43 am
回答 (2)
2007-10-08 10:57 am
✔ 最佳答案
2) Consider four numbers 27, x, y, 6.(a) Given that the first three numbers form a geometric sequence, express y in terms of x.
即是話頭3 個數27, x, y 組成一個G.P. 要你列條式代表y 同 x 既關係
common ratio = 27/x=x/y
so, 27/x=x/y
27y=x^2
y=x^2/27
(b) Given that the last three numbers form a arithmetic sequence, express y in terms of x.
即是話尾3 個數 x, y, 6 組成一個A.P. 要你列條式代表y 同 x 既關係
common difference = x-y=y-6
so, x-y=y-6
2y=x+6
y=(x+6)/2
2007-10-08 7:02 am
1)(a)
a+ar^2=250-----(1)
ar^2+ar^4=2250-----(2)
a(1+r^2)=250-----(1)
a(r^2+r^4)=2250-----(2)
(2)/(1)
(r^2+r^4)/(1+r^2)=2250/250
(r^2+r^4)/(1+r^2)=9
(r^2+r^4)=9+9r^2
r^4-8r^2-9=0
(r^2-9)(r^2+1)=0
r^2=9 r^2=-1(rejected)
r=3 or -3
1)(b)
a+a(3^2)=250
10a=250
a=25
Question 2 i don't understand what is asking for,
sorry...
a+ar^2=250-----(1)
ar^2+ar^4=2250-----(2)
a(1+r^2)=250-----(1)
a(r^2+r^4)=2250-----(2)
(2)/(1)
(r^2+r^4)/(1+r^2)=2250/250
(r^2+r^4)/(1+r^2)=9
(r^2+r^4)=9+9r^2
r^4-8r^2-9=0
(r^2-9)(r^2+1)=0
r^2=9 r^2=-1(rejected)
r=3 or -3
1)(b)
a+a(3^2)=250
10a=250
a=25
Question 2 i don't understand what is asking for,
sorry...
收錄日期: 2021-04-23 17:18:11
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