if x,a,b,c,d,y are six consecutive terms of an arithmetic sequence, prove:
(a) a+b+c+d=2(x+y)
(b) (y-x) / (c-b) =5
有關arithmetic sequence的問題
2007-10-21 5:07 pm
回答 (2)
2007-10-21 5:16 pm
✔ 最佳答案
(a) Let A is the first term , d is common differencex = A, a = A + d, b = A + 2d, c = A + 3d, d = A + 4d, y = A + 5d
(a) a+b+c+d
= (A+d) + (A+2d) +(A+3d) +(A+4d)
= 4A+ 10d
2(x+y )
=2 (A + A+5d)
= 4A + 10d
= a+b+c+d
(b) (y-x) / (c-b)
=(A+5d - A) / (A + 3d - A-2d)
= 5d/d
= 5
參考: My calculation
2007-10-21 5:15 pm
Let k be the difference in the arithmetic sequence, we have
a = x + k
b = x + 2k
c = x + 3k
d = x + 4k
y = x + 5k
a)
LHS = a + b + c + d = 4x + (k + 2k + 3k + 4k) = 4x + 10k
RHS = 2(x + y) = 2(2x + 5k) = 4x + 10k
b)
y - x = x + 5k - x = 5k
c - b = (x + 3k) - (x + 2k) = k
(y - x) / (c - b) = 5k / k = 5
a = x + k
b = x + 2k
c = x + 3k
d = x + 4k
y = x + 5k
a)
LHS = a + b + c + d = 4x + (k + 2k + 3k + 4k) = 4x + 10k
RHS = 2(x + y) = 2(2x + 5k) = 4x + 10k
b)
y - x = x + 5k - x = 5k
c - b = (x + 3k) - (x + 2k) = k
(y - x) / (c - b) = 5k / k = 5
參考: myself
收錄日期: 2021-04-13 14:04:06
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071021000051KK00778