sequence

2012-05-21 5:54 am
1. the interior angel of a hexagon form an arithmetic sequence. find the sum of the smallest angle and the largest angle.

A. 180
B. 220
C. 240
D. 360

要步驟謝謝,答案是240,忘記了怎樣計。
2.
1+2+2^2+2^3+...+2^=?
A. 2^n-1
B. 2^(n+1)-1
C.(2^n-1)/2
D.(2^(n+1)-1)/2
我認為答案是B,但是SOLUTION係C.到底是我錯還是SOL印錯?

回答 (2)

2012-05-21 6:26 am
✔ 最佳答案
1.
Let a be the smallest angle, then the other angles are a+d, a+2d, ... , a+5d.
Total sum of interior angles = [a + (a+5d)]x6 / 2 ... {頭加尾乘項數除2 } = (6-2)180deg ... (內角和 = (邊-2)X180度 )
6a + 15d = 720
2a + 5d = 240
smallest angle + largest angle
= a + (a+5d)
= 2a + 5d
=240 deg
Ans: C

2. 最後那個是2^n吧... 答案是B...
參考: MYSELF
2012-05-21 6:16 am
The last term 2^ is what ?

2012-05-20 22:16:58 補充:
1)Let 6 angles be x - 1.5 , x - 1 , x - 0.5 , x + 0.5 , x + 1 , x + 1.5 ,then sum of the angles :6x = (6 - 2)180°
x = 120°The sum of the smallest angle and the largest angle
= x -1.5 + x+1.5
= 2x
= 240°Choose (C).
2)Assuming that the question is 1 + 2 + 2² + 2³ + ... + 2ⁿ ,1st term a = 1
common ratio r = 2Sum of G.S. of the first n terms = a(1 - rⁿ) / (1 - r)
In this case , there are n+1 terms , 1(1 - 2ⁿ⁺¹) / (1 - 2)= 2ⁿ⁺¹ - 1 Choose B , you are right ~I think it is impossible for the answer is C since it is not a odd number.

2012-05-20 22:18:41 補充:
Corr:

Line 2 should be :

Let 6 angles be x - 2.5 , x - 1.5 , x - 0.5 , x + 0.5 , x + 1.5 , x + 2.5 ,

2012-05-20 22:26:34 補充:
Corrections for Q1)

Let 6 angles be x - 5d , x - 3d , x - d , x + d , x + 3d , x + 5d ,(the common difference is 2d)

then sum of the angles :

6x = (6 - 2)180°
x = 120°

The sum of the smallest angle and the largest angle
= x -5d + x+5d
= 2x
= 240°

Choose (C).

I'm sorry!




I'm sorry again!


收錄日期: 2021-04-21 22:24:26
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120520000051KK00656

檢視 Wayback Machine 備份